The militant leader was himself convicted in 2004 of plotting attacks on Jordanian air bases hosting American trainers, but served his term and was released last year.
Militants linked to al-Qaida, many from Iraq but also reportedly several from Jordan, are believed to have made inroads among Syrian rebels as the civil war their intensifies.
The warning came hours after Syrian Foreign Ministry spokesman Jihad Makdessi criticized France, saying its growing support for the opposition does nothing but undermine the mission of the new U.N. envoy tasked with brokering a diplomatic solution to the conflict.
France, Syria's one-time colonial ruler, has been one of the most outspoken Western critics of the Assad regime, and announced earlier this month that it has begun sending direct aid and money to five rebel-held Syrian cities as part of its intensified efforts to weaken Assad. It was the first such move by a Western power amid mounting calls for the international community to do more to prevent bloodshed.
Makdessi said France suffers from "schizophrenia" in its approach to the country's conflict.
"On the one hand, it supports Brahimi's mission, while at the same time it makes statements demonstrating that it supports the militarization of the crisis in Syria," Makdessi told The Associated Press.