The report says FBI chief Robert Mueller promised to strengthen cooperation with the country on the southern edge of the Arabian Peninsula where an al-Qaida offshoot has taken root.
The report was quoting a statement from President Ali Abdullah Saleh's office.
Al-Qaida in the Arabian Peninsula is believed to have built up strongholds in remote parts of Yemen, allying with powerful tribes that resent Saleh's government. The group claimed responsibility for the failed Christmas Day attempt to bomb an American airliner heading for Detroit.
Washington has stepped up counterterrorism aid to Yemen over the past year.