EXHIBIT 32.1

CERTIFICATE OF THE CHIEF EXECUTIVE OFFICER

OF HARKEN ENERGY CORPORATION (REGISTRANT)

Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 (18 U.S.C.ss. 1350):

I, Mikel D. Faulkner, Chief Executive Officer of the Registrant, certify to the best of my knowledge and belief pursuant to Section 906 of Sarbanes-Oxley Act of 2002 (18 U.S.C.ss. 1350) that:

(1) The Quarterly Report on Form 10-Q for the period ended March 31, 2004, which this statement 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 Quarterly Report on Form 10-Q fairly presents, in all material respects, the financial condition and result of operations of the Registrant.

Date: May 13, 2004

/s/    MIKEL D. FAULKNER        

Chief Executive Officer