Exhibit 32.1

URANIUM RESOURCES, INC.
650 S. Edmonds Lane, Suite 108, Lewisville, TX 75067
972.219.3330 Phone 972.219.3311 Fax

May 14, 2004

Securities and Exchange Commission
450 5^th Street, N.W.
Washington, D.C. 20549

CERTIFICATION OF CHIEF EXECUTIVE OFFICER
PURSUANT TO SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

I, Paul K. Willmott, President and Chief Executive Officer of Uranium Resources, Inc. (the "Company"), certify, pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that to my knowledge:

(1)

The Quarterly Report on Form 10-QSB of the Company for the period ended March 31, 2004 which this certification accompanies fully complies with the requirements of section 13(a) or 15(d) 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.

/s/  PAUL K. WILLMOTT Paul K. Willmott
President and Chief Executive Officer
May 14, 2004