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 I, T. Paul Bulmahn, Chairman and Chief Executive Officer of ATP Oil & Gas Corporation (the "Company"), do hereby certify that the Quarterly Report on Form 10-Q (the "Report") for the quarter ended September 30, 2003, filed with the Securities Exchange Commission on the date hereof: 1) 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 represents, in all material respects, the financial condition and the results of operations of the Company. Date: November 17, 2003 By: /s/ T. Paul Bulmahn ------------------------------------- T. Paul Bulmahn Chairman, Chief Executive Officer and President