Exhibit 99.1

MESABI TRUST

PRESS RELEASE

New York, New York

April 12, 2013

The Trustees of Mesabi Trust (NYSE: MSB) declared a distribution of eight cents ($0.08) per Unit of Beneficial Interest payable on May 20, 2013 to Mesabi Trust unitholders of record at the close of business on April 30, 2013. This compares to a distribution of six and one-half cents ($0.065) per Unit for the same period last year.

The one and one-half cent ($0.015) per Unit increase over the same period last year is primarily attributable to a reduction in the amount of negative price adjustments to royalties previously received by Mesabi Trust. In the first calendar quarter of each year, Northshore Mining Company (“Northshore”), the lessee/operator of the mine on Mesabi Trust lands, calculates adjustments to pricing on tons shipped from Northshore during the prior calendar year and applies those adjustments, which can be positive or negative, to the royalties payable to Mesabi Trust for the first calendar quarter of the current year.  In the first quarter of 2013, Northshore applied $479,831 of negative price adjustments against royalties payable to Mesabi Trust, as compared to $984,546 of negative price adjustments in the first quarter of 2012.  During the three months ended March 31, 2013, there were decreases in the volume of shipments of iron ore pellets shipped by Northshore and the average sales price, each as compared to the same period last year, thereby reducing the overall cash available for distribution.  The lower volume of shipments of iron ore pellets and lower average sales prices per ton resulted in the total royalty amount decreasing from approximately $2.15 million in the first calendar quarter of 2012 to approximately $1.62 million for the first calendar quarter of 2013, before application of the negative price adjustments by Nothshore.

Based on shipments of iron ore pellets during the three months ending March 31, 2013, as reported by Northshore, Mesabi Trust expects to be paid a base royalty of $676,242 on April 30, 2013.  Mesabi Trust also expects to be paid a bonus royalty in the amount of $811,490 based on the average sales price per ton of iron ore pellets and the volume of shipments during the first calendar quarter of 2013.  Negative price adjustments for the calendar year 2012 generated a decrease in base and bonus royalty payment of $479,831.  The total royalty payment expected to be received by Mesabi Trust on April 29, 2013 is $1,147,301 (including a royalty payment of $139,400 payable to the Mesabi Land Trust) after giving effect to all price adjustments applied by Northshore in the current calendar quarter.

Royalties paid to Mesabi Trust are based on the volume of shipments of iron ore pellets for the quarter and the year to date, the pricing of the iron ore product sales, and the percentage of iron ore pellet shipments from Mesabi Trust lands rather than from non-Trust lands.  In the first calendar quarter of 2013, Northshore credited Mesabi Trust with 345,073 tons of iron ore, as compared to 388,094 tons credited from Mesabi Trust lands during the first calendar quarter of 2012. Although Mesabi Trust was credited with shipments of 345,073 tons of iron ore during the first calendar quarter of 2013 (because it is entitled to payment on at least 90% of the first four million tons of pellets shipped from Silver Bay, MN by Northshore in each calendar year), actual shipments of iron ore products shipped from Mesabi Trust lands in the first calendar quarter of 2013 were 313,268 tons.  The volume of shipments of iron

ore pellets (and other iron ore products) by Northshore varies from quarter to quarter and year to year based on a number of factors, including the requested delivery schedules of customers, general economic conditions in the iron ore industry, and weather conditions on the Great Lakes. Further, the prices under the term contracts between Northshore, Cliffs Natural Resources Inc., Northshore’s parent company (“Cliffs”), and certain of their customers (the “Cliffs Pellet Agreements”), to which Mesabi Trust is not a party, are subject to interim and final pricing adjustments, dependent in part on multiple price and inflation index factors that are not known until after the end of a contract year.  This can result in significant variations in royalties received by Mesabi Trust (and in turn the resulting amount available for distribution to Unitholders by Mesabi Trust) from quarter to quarter and on a comparative historical basis. These variations, which can be positive or negative, cannot be predicted by the Trustees of Mesabi Trust. Royalty payments received in 2013 and prior years continue to reflect pricing estimates for shipments of iron ore products that were subject to negative pricing adjustments pursuant to the Cliffs Pellet Agreements.  Based on the above factors and as indicated by the Trust’s historical distribution payments, the royalties received by the Trust, and the distributions paid to Unitholders, in any particular quarter are not necessarily indicative of royalties that will be received, or distributions that will be paid, in any subsequent quarter or for a full year.

With respect to the remainder of calendar year 2013, Northshore has not advised Mesabi Trust of its expected 2013 shipments of iron ore products or what percentage of 2013 shipments will be from Mesabi Trust iron ore.  Cliffs has not provided Mesabi Trust with any projections about possible pricing (and resulting royalty) adjustments that might impact future distributions, although Cliffs did indicate that the royalty payments being reported today are based on estimated iron ore pellet prices under the Cliffs Pellet Agreements, which are subject to change.  It is possible that future negative price adjustments could offset, or even eliminate, royalties or royalty income that would otherwise be payable to Mesabi Trust in any particular quarter, or at year end, thereby potentially reducing cash available for distribution to Mesabi Trust’s Unitholders in future quarters.   In addition, because the Cliffs Pellet Agreements contain various pricing formulas and price adjustment provisions, the average sales prices received by Mesabi Trust may not match international iron ore pellet prices.

This press release contains certain forward-looking statements with respect to iron ore pellet production, iron ore pricing and adjustments to pricing, shipments by Northshore in 2013, royalty (including bonus royalty) amounts, and other matters, which statements are intended to be made under the safe harbor protections of the Private Securities Litigation Reform Act of 1995, as amended. Actual production, prices, price adjustments, and shipments of iron ore pellets, as well as actual royalty payments (including bonus royalties) could differ materially from current expectations due to inherent risks such as general and industry economic trends, uncertainties arising from war, terrorist events and other global events, higher or lower customer demand for steel and iron ore, environmental compliance uncertainties, higher imports of steel and iron ore substitutes, processing difficulties, consolidation and restructuring in the domestic steel market, indexing features in Cliffs Pellet Agreements resulting in adjustments to royalties payable to Mesabi Trust and other factors. Further, substantial portions of royalties earned by Mesabi Trust are based on estimated prices that are subject to interim and final adjustments, which can be positive or negative, and are dependent in part on multiple price and inflation index factors under agreements to which Mesabi Trust is not a party and that are not known until after the end of a contract year. Although the Mesabi Trustees believe that any such forward-looking statements are based on reasonable assumptions, such statements are subject to risks and uncertainties, which could cause actual results to differ materially.  Additional information concerning

these and other risks and uncertainties is contained in the Trust’s filings with the Securities and Exchange Commission, including its Annual Report on Form 10-K.  Mesabi Trust undertakes no obligation to publicly update or revise any of the forward-looking statements that may be in this press release.