Former CIA Director David Petraeus and the U.S. intelligence community extensively researched the Syrian opposition, ensuring that most of the American weapons provided to the rebels will not reach al Qaeda groups, according to Sen. Bob Corker.

"That's the second war that so many of us have talked about, and that is, after [Syrian dictator Bashar] Assad, who is going to control the country?" the Tennessee Republican said on CBS's "Face the Nation."

"So, look, I think we know more than we let on publicly about which groups to support and which not. We need to do much more to help them. Our intelligence agencies, I think, have a very good handle on who to support and who not to support," he said.

Still, Corker acknowledged that the vetting is imperfect, some weapons will likely be sent to enemy groups.

"[T]here's going to be mistakes," the top Republican on the Senate Foreign Relations Committee said. "We understand some people are going to get arms that should not be getting arms. But we still should be doing everything we can to support the free Syrian opposition."

Senate Armed Services Committee Chairman Carl Levin, D-Mich., also endorsed providing weapons — he expects the Obama team to provide anti-tank weapons, in particular — to the Syrian opposition groups.

Levin also rejected Assad's latest demand. "Syria has tried very hard and will continue to try to make it a condition of its compliance with this agreement between Russia and the United States that the United States not support the opposition," he said. "We are not going to agree to that."