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SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM 10-Q

(Mark One)

For the quarterly period ended March 31, 2003

OR

For the transition period from                                               to                                              

Commission file number 0-49633

WELLS REAL ESTATE FUND XIII, L.P.

(Exact name of registrant as specified in its charter)

(Former name, former address and former fiscal year, if changed since last report)

Indicate by check mark whether the registrant (1) has filed all reports required to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during the preceding 12 months (or for such shorter period that the registrant was required to file such reports), and (2) has been subject to such filing requirements for the past 90 days.

Yes x No ¨

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FORM 10-Q

WELLS REAL ESTATE FUND XIII, L.P.

(A Georgia Public Limited Partnership)

INDEX

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WELLS REAL ESTATE FUND XIII, L.P.

(A Georgia Public Limited Partnership)

BALANCE SHEETS

See accompanying notes.

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WELLS REAL ESTATE FUND XIII, L.P.

(A Georgia Public Limited Partnership)

STATEMENTS OF INCOME

See accompanying notes.

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WELLS REAL ESTATE FUND XIII, L.P.

(A Georgia Public Limited Partnership)

STATEMENTS OF PARTNERS’ CAPITAL

FOR THE YEARS ENDED DECEMBER 31, 2002

AND THE THREE MONTHS ENDED MARCH 31, 2003 (UNAUDITED)

See accompanying notes.

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WELLS REAL ESTATE FUND XIII, L.P.

(A Georgia Public Limited Partnership)

STATEMENTS OF CASH FLOWS

See accompanying notes.

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WELLS REAL ESTATE FUND XIII, L.P.

(A Georgia Public Limited Partnership)

CONDENSED NOTES TO FINANCIAL STATEMENTS

MARCH 31, 2003 (UNAUDITED)

(a) Organization and Business

Wells Real Estate Fund XIII, L.P. (the “Partnership”) is a Georgia public limited partnership with Leo F. Wells, III and Wells Capital, Inc. (the “Company”), a Georgia corporation, serving as General Partners. The Partnership was formed on September 15, 1998, for the purpose of acquiring, developing, owning, operating, improving, leasing, and otherwise managing income producing commercial properties for investment purposes. Upon subscription for units, the Limited Partners must elect whether to have their units treated as Cash Preferred Status Units or Tax Preferred Status Units. Thereafter, Limited Partners have the right to change their prior elections to have some or all of their units treated as Cash Preferred Status Units or Tax Preferred Status Units one time during each quarterly accounting period. Limited Partners may vote to, among other things: (a) amend the partnership agreement, subject to certain limitations, (b) change the business purpose or investment objectives of the Partnership, (c) remove a General Partner, (d) elect a new General Partner, (e) dissolve the Partnership, and (f) approve a sale involving all or substantially all of the Partnership’s assets, subject to certain limitations. The majority vote on any of the described matters will bind the Partnership, without the concurrence of the General Partners. Each limited partnership unit has equal voting rights, regardless of which class of unit is selected.

On March 29, 2001, the Partnership commenced a public offering of up to $45,000,000 of limited partnership units ($10.00 per unit) pursuant to a Registration Statement filed on Form S-11 under the Securities Act of 1933. The Partnership commenced active operations on June 14, 2001, upon receiving and accepting subscriptions for 125,000 units. The offering was terminated on March 28, 2003, at which time the Partnership had sold 3,027,449 Cash Preferred Units and 748,713 Tax Preferred Units, net of conversions, held by a total of 1,276 and 144 limited partners, respectively, for total Limited Partner capital contributions of $37,761,615. After payment of $1,409,592 in acquisition and advisory fees and acquisition expenses, payment of $4,014,806 in selling commissions and organization and offering expenses, and the investment of $16,729,212 in Fund XIII-REIT Associates (“the Joint Venture”), as of March 31, 2003, the Partnership was holding net offering proceeds of $15,608,005 available for investment in properties.

The Partnership was formed to acquire and operate commercial real estate properties, including properties which are either to be developed, are currently under development or construction, are newly constructed, or have operating histories.

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As of March 31 2003, the Partnership owned interests in the following three properties through the affiliated Joint Venture listed below:

Each of the aforementioned properties was acquired on an all cash basis. For further information regarding the foregoing joint ventures and properties, refer to the report filed for the Partnership on Form 10-K for the year ended December 31, 2002.

(b) Basis of Presentation

The financial statements of the Partnership have been prepared in accordance with the rules and regulations of the Securities and Exchange Commission, including the instructions to Form 10-Q and Article 10 of Regulation S-X, and in accordance with such rules and regulations, do not include all of the information and footnotes required by accounting principles generally accepted in the United States (“GAAP”) for complete financial statements. The quarterly statements have not been examined by independent auditors. However, in the opinion of the General Partners, the statements for the unaudited interim periods presented include all adjustments that are of a normal and recurring nature and necessary to fairly present the results for these periods. Results for interim periods are not necessarily indicative of full year results. For further information, refer to the financial statements and footnotes included in the Partnership’s Form 10-K for the year ended December 31, 2002.

(c) Allocation of Net Income, Net Loss, and Gain on Sale

For the purposes of determining allocations per the Partnership agreement, net income is defined as net income recognized by the Partnership, excluding deductions for depreciation and amortization. Net income, as defined, of the Partnership will be allocated each year in the same proportions that net cash from operations is distributed to the limited partners holding Class A units and the general partners. To the extent the Partnership’s net income in any year exceeds net cash from operations, it will be allocated 99% to the limited partners and 1% to the general partners.

Net loss, depreciation, and amortization deductions for each fiscal year will be allocated as follows: (a) 99% to the limited partners holding tax preferred units and 1% to the general partners until their capital accounts are reduced to zero, (b) then to any partner having a positive balance in his/her capital account in an amount not to exceed such positive balance, and (c) thereafter to the general partners.

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Gain on the sale or exchange of the Partnership’s properties will be allocated generally in the same manner that the net proceeds from such sale are distributed to partners after the following allocations are made, if applicable: (a) allocations made pursuant to the qualified income offset provisions of the partnership agreement, (b) allocations to partners having negative capital accounts until all negative capital accounts have been restored to zero, and (c) allocations to limited partners holding tax preferred units in amounts equal to the deductions for depreciation and amortization previously allocated to them with respect to the specific partnership property sold, but not in excess of the amount of gain on sale recognized by the Partnership with respect to the sale of such property.

(d) Distribution of Net Cash From Operations

As defined by the partnership agreement, cash available for distribution is distributed quarterly to the limited partners as follows:

No distributions will be made to the limited partners holding Tax Preferred Units.

(e) Distribution of Sale Proceeds

Upon the sale of properties, the net sale proceeds will be distributed in the following order:

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(a) Basis of Presentation

As of March 31, 2003, the Partnership owned interests in three properties through its ownership in the Joint Venture described in Note 1. The Partnership does not have control over the operations of the Joint Venture; however, it does exercise significant influence. Accordingly, investments in the Joint Venture are recorded using the equity method of accounting, whereby original investments are recorded at cost and subsequently adjusted for contributions, distributions and net income (loss) attributable to the Partnership. For further information regarding investments in Joint Venture, see the report filed for the Partnership on Form 10-K for the year ended December 31, 2002.

(b) Summary of Operations

The following information summarizes the operations of the Joint Venture, in which the Partnership held an ownership interest for the three months ended March 31, 2003 and 2002, respectively:

On January 1, 2002, the Partnership adopted Statement of Financial Accounting Standards No. 141 “Business Combinations,” and Statement of Financial Accounting Standards No. 142 “Goodwill and Intangibles.” These standards govern business combinations and asset acquisitions, and the accounting for acquired intangibles. The Partnership determines whether an intangible asset or liability related to above or below market leases was acquired as part of the acquisition of real estate assets. The resulting intangible lease assets and liabilities are recorded at their estimated fair market values at the date of acquisition and amortized over the remaining term of the respective lease to

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rental income.

In January 2003, the Financial Accounting Standards Board issued Interpretation No. 46 (FIN 46), “Consolidation of Variable Interest Entities,” which clarifies the application of Accounting Research Bulletin (ARB) No. 51, “Consolidated Financial Statements,” relating to consolidation of certain entities. FIN 46 will require the identification of the Partnership’s participation in variable interest entities (VIEs), which are defined as entities with a level of invested equity that is not sufficient to fund future activities to permit them to operate on a stand alone basis, or whose equity holders lack certain characteristics of a controlling financial interest. For entities identified as VIEs, FIN 46 sets forth a model to evaluate potential consolidation based on an assessment of which party to the VIE, if any, bears a majority of the exposure to its expected losses, or stands to gain from a majority of its expected returns. FIN 46 is effective for all new VIEs created or acquired after January 31, 2003. For VIEs created or acquired prior to February 1, 2003, the provisions of FIN 46 must be applied for the first interim or annual period beginning after June 15, 2003. FIN 46 also sets forth certain disclosures regarding interests in VIEs that are deemed significant, even if consolidation is not required. As the Joint Ventures do not fall under the definition of VIEs provided above, the Partnership does not believe that the adoption of FIN 46 will result in the consolidation of any previously unconsolidated entities.

In August 2001, SFAS No. 144, “Accounting for the Impairment or Disposal of Long-Lived Assets” (effective beginning January 1, 2002) was issued. SFAS No. 144 addresses financial accounting and reporting for the impairment of long-lived assets and for long-lived assets to be disposed of and supersedes SFAS No. 121, “Accounting for the Impairment of Long-Lived Assets and for Long-Lived Assets to be Disposed of”. Among other factors, SFAS No. 144 establishes criteria beyond that previously specified in SFAS No. 121 to determine when a long-lived asset is to be considered held for sale. We believe that the adoption of SFAS No. 144 will not have a significant impact on our financial statements.

Management and Leasing Fees

Wells Management Company, Inc., (“Wells Management”), an affiliate of the General Partners, receives compensation for supervising the management and leasing of the Partnership’s properties owned through joint ventures equal to the lesser of (a) fees that would be paid to a comparable outside firm or (b) 4.5% of the gross revenues generally paid over the life of the lease plus a separate competitive fee for the one-time initial lease-up of newly constructed properties generally paid in conjunction with the receipt of the first month’s rent. In the case of commercial properties which are leased on a long-term net basis (ten or more years), the maximum property management fee from such leases shall be 1% of the gross revenues generally paid over the life of the leases except for a one-time initial leasing fee of 3% of the gross revenues on each lease payable over the first five full years of the original lease term. For the three months ended March 31, 2003 and 2002, the properties in which the partnership owns interests paid management and leasing fees to Wells Management of $56,365 and $23,829, respectively.

Administration Reimbursements

Wells Capital, Inc. performs certain administrative services for the Partnership, such as accounting and other partnership administration, and incurs the related expenses. Such expenses are allocated among the various Wells Real Estate Funds based on time spent on each fund by individual administrative personnel. For the three months ended March 31, 2003 and 2002, the Partnership

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reimbursed $35,238 and $12,824, respectively, to Wells Capital, Inc. and its affiliates for these services.

Conflicts of Interests

The General Partners are also general partners of other Wells Real Estate Funds. As such, there may exist conflicts of interest where the general partners in their capacity as general partners of other Wells Real Estate Funds may be in competition with the Partnership in connection with property acquisitions or for tenants in similar geographic markets.

The following discussion and analysis should be read in conjunction with the accompanying financial statements and notes thereto.

(a) Forward-Looking Statements

This report contains forward-looking statements within the meaning of Section 27A of the Securities Act of 1933 and 21E of the Securities Exchange Act of 1934, including discussion and analysis of the financial condition of the Partnership, anticipated capital expenditures required to complete certain projects, amounts of cash distributions anticipated to be distributed to limited partners in the future and certain other matters. Readers of this Report should be aware that there are various factors that may cause actual results to differ materially from any forward-looking statements made in this report, including construction costs which may exceed estimates, construction delays, lease-up risks, inability to obtain new tenants upon the expiration of existing leases, and the potential need to fund tenant improvements or other capital expenditures out of operating cash flows.

(b) Results of Operations

Gross Revenues

Gross revenues of the Partnership increased to $280,162 for the three months ended March 31, 2003, from $136,116 for the three months ended March 31, 2002, primarily due to the corresponding increases in (i) interest income as a result of holding additional investor proceeds during the first quarter of 2003, as compared to the first quarter of 2002, and (ii) operating cash flows generated by the Joint Venture, which is further described below. The Partnership commenced operations on June 14, 2001, and made an initial investment in the Joint Venture on June 27, 2001. As of March 31, 2003, the Joint Venture has invested in three income producing properties as further discussed below.

Equity In Income of Joint Venture

Gross Revenues of Joint Venture

Gross revenues of the Joint Venture in which the Partnership holds an interest increased in 2003, as compared to 2002, primarily due to the acquisition of the John Wiley Building in December 2002.

Expenses of Joint Venture

The expenses of the Joint Venture in which the Partnership holds an interest increased in 2003, as compared to 2002, primarily due to an increase in: (i) accounting and legal fees incurred in connection with changing independent auditors in 2002, (ii) amortization of an intangible lease asset and operating expenses incurred in connection with the acquisition of the John Wiley Building in December 2002.

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Expenses

Expenses of the Partnership increased to $52,616 for 2003, as compared to $21,997 for 2002, primarily due to increases in administrative costs and expenses and accounting fees related to the termination of the offering of sale of limited partnership units to the public effective March 28, 2003.

As a result, net income of the Partnership was $227,546 and $114,119 for the three months ended March 31, 2003 and 2002, respectively.

(c) Liquidity and Capital Resources

Cash Flows From Operating Activities

Net cash flows from operating activities remained relatively stable at $(95,069) for the three months ended March 31, 2003 as compared to $(94,265) for the three months ended March 31, 2002.

Cash Flows From Investing Activities

Net cash flows from investing activities was $(72,710) and $(50,033) for the three months ended March 31, 2003 and 2002, respectively. As the offering of the Partnership’s units commenced on March 29, 2001 and terminated on March 28, 2003, more capital was raised in 2003, as compared to 2002, thus, resulting in the payment of additional deferred project costs in 2003, as compared to 2002, offset by the receipt of additional distributions from Fund XIII-REIT Associates in 2003, as compared to 2002, due to the acquisition of John Wiley Building in December 2002.

Cash Flows From Financing Activities

Net cash flows provided by financing activities increased to $9,176,888 for 2003, as compared to $2,777,732 for 2002, as a result of raising additional capital in 2003, which is partially offset by the payment of additional related selling commissions and offering cost reimbursements and distributions to more limited partners in 2003, as compared to 2002.

Distributions

The Partnership made distributions to the limited partners holding Cash Preferred Units of $0.12 per unit, $0.16 per unit for the three months ended March 31, 2003 and 2002, respectively. Such distributions have been made from net cash from operations and distributions received from the Partnership’s investment in joint venture. Distributions accrued for the first quarter of 2003 to the Limited Partners holding Cash Preferred Units were paid in May 2003. No cash distributions were made to Limited Partners holding Tax Preferred Units.

Capital Resources

The Partnership is an investment vehicle formed for the purpose of acquiring, owning and operating income-producing real properties and is currently holding approximately $15 million of funds that are available for investment. Accordingly, the Partnership intends to invest all of such funds into additional investment properties and is actively seeking prospective property acquisitions. Other than those mentioned above, the General Partners are unaware of any specific need requiring capital resources.

(d) Related Party Transactions and Agreements

The Partnership and its joint venture have entered into agreements with Wells Capital, Inc. and its affiliates, whereby they pay certain fees or reimbursements to Wells Capital, Inc. or its affiliates (e.g. property management and leasing fees, administrative salary reimbursements, etc.). See Note 4 to the

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Partnership’s financial statements included in this report for a discussion of the various related party transactions, agreements, and fees.

(e) Inflation

The real estate market has not been affected significantly by inflation in the past three years due to the relatively low inflation rate. However, there are provisions in the majority of tenant leases, which would protect the Partnership from the impact of inflation. These provisions include reimbursement billings for operating expense pass-through charges, real estate tax and insurance reimbursements on a per square foot basis, or in some cases, annual reimbursement of operating expenses above a certain per square foot allowance. There is no assurance, however, that the Partnership would be able to replace existing leases with new leases at higher base rental rates.

(f) Application of Critical Accounting Policies

The Partnership’s accounting policies have been established to conform with GAAP. The preparation of financial statements in conformity with GAAP requires management to use judgment in the application of accounting policies, including making estimates and assumptions. These judgments affect the reported amounts of assets and liabilities and disclosure of contingent assets and liabilities at the dates of the financial statements and the reported amounts of revenue and expenses during the reporting periods. If management’s judgment or interpretation of the facts and circumstances relating to various transactions had been different, it is possible that different accounting policies would have been applied; thus, resulting in a different presentation of the financial statements. Additionally, other companies may utilize different estimates that may impact comparability of the Partnership’s results of operations to those of companies in similar businesses.

Below is a discussion of the accounting policies that management considers to be critical in that they may require complex judgment in their application or require estimates about matters that are inherently uncertain.

Investment in Real Estate Assets

Management is required to make subjective assessments as to the useful lives of its depreciable assets. Management considers the period of future benefit of the asset to determine the appropriate useful lives. These assessments have a direct impact on net income. The estimated useful lives of the Joint Venture’s assets by class are as follows:

In the event that management uses inappropriate useful lives or methods for depreciation, the Partnership’s net income would be misstated.

Valuation of Real Estate Assets

Management continually monitors events and changes in circumstances that could indicate that the carrying amounts of the real estate assets in which the Partnership has an ownership interest, either directly or through investments in joint ventures, may not be recoverable. When indicators of potential impairment are present which indicate that the carrying amounts of real estate assets may not be recoverable, management assesses the recoverability of the real estate assets by determining whether the carrying value of the real estate assets will be recovered through the undiscounted future

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operating cash flows expected from the use of the asset and its eventual disposition. In the event that such expected undiscounted future cash flows do not exceed the carrying value, management adjusts the real estate assets to the fair value and recognizes an impairment loss. Management has determined that there has been no impairment in the carrying value of real estate assets held by the Partnership to date.

Projections of expected future cash flows requires management to estimate future market rental income amounts subsequent to the expiration of current lease agreements, property operating expenses, discount rates, the number of months it takes to re-lease the property, and the number of years the property is held for investment. The use of inappropriate assumptions in the future cash flow analysis would result in an incorrect assessment of the property’s future cash flows and fair value, and could result in the overstatement of the carrying value of real estate assets held by the joint ventures and net income of the Partnership.

Intangible Lease Asset/Liability

The Partnership determines whether an intangible asset or liability related to above or below market leases was acquired as part of the acquisition of the real estate assets, either directly or through the Joint Venture. The intangible assets and liabilities are recorded at their estimated fair market values at the date of acquisition and amortized over the remaining term of the respective lease to rental income.

The determination of the estimated fair values of the intangible lease asset or liability requires the use of significant assumptions with regard to the current market rental rates, rental growth rates, discount rates and other variables. If inappropriate estimates with regard to these variables are used, misclassification of assets or liabilities and incorrect calculation of depreciation amounts would occur, which would misstate our net income.

Since the Partnership does not borrow any money, make any foreign investments or invest in any market risk sensitive instruments, it is not subject to risks relating to interest rates, foreign current exchange rate fluctuations or the other market risks contemplated by Item 305 of Regulation S-K.

Within the 90 days prior to the date of this report, the Partnership carried out an evaluation, under the supervision and with the participation of management of Wells Capital, Inc., the corporate General Partner of the Partnership, including the Principal Executive Officer and Principal Financial Officer, of the effectiveness of the design and operation of the Partnership’s disclosure controls and procedures pursuant to Rule 13a-14 under the Securities Exchange Act of 1934. Based upon that evaluation, the Principal Executive Officer and Principal Financial Officer concluded that the Partnership’s disclosure controls and procedures were effective.

There were no significant changes in the Partnership’s internal controls or other factors that could significantly affect such controls subsequent to the date of their evaluation.

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PART II.    OTHER INFORMATION

SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934, the Registrant duly caused this report to be signed on its behalf by the undersigned thereunto duly authorized.

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CERTIFICATIONS

I, Leo F. Wells, III, certify that:

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CERTIFICATIONS

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EXHIBIT INDEX

TO

FIRST QUARTER FORM 10-Q

OF

WELLS REAL ESTATE FUND XIII, L.P.

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