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 Teleglobe International Holdings Ltd (the “Company”) on Form 10-Q for the quarter ended June 30, 2004, filed with the Securities and Exchange Commission (the “Report”), I, Gerald Porter Strong, Chief Executive Officer of the Company, certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

(1) The Report fully complies with the requirements of Section 13(a) of the Securities Exchange Act of 1934; and

(2) The information contained in the Report fairly presents, in all material respects, the consolidated financial condition of the Company as of the dates presented and the consolidated result of operations of the Company for the periods presented.

Dated: October 15, 2004

/s/    GERALD PORTER STRONG        

Gerald Porter Strong

Chief Executive Officer and President of

Teleglobe International Holdings Ltd

This certification has been furnished solely pursuant to Section 906 of the Sarbanes-Oxley Act of 2002.