EXHIBIT 32.1

CERTIFICATION PURSUANT TO
18 U.S.C. SECTION 1350,
AS ADOPTED PURSUANT TO
SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report of AmREIT Monthly Income & Growth Fund III, Ltd. (the “Company”) on Form 10-Q for the period ended June 30, 2013, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, H. Kerr Taylor, certify, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, in my capacity as an officer of the General Partner of the Company, that, to my knowledge:

1. The Report fully complies with the requirements of section 13(a) or 15(d), as applicable, of the Securities Exchange Act of 1934; and
2. The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.