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Sen. Corker: U.S. support to rebels will likely fall into terrorists' hands

American weapons being supplied to Syria's rebels will likely fall into the hands of terror groups fighting alongside opposition forces there, Sen. Bob CorkerRobert (Bob) Phillips CorkerCornyn: Relationships with Trump like 'women who get married and think they're going to change their spouse' Trump excoriates Sasse over leaked audio Has Congress captured Russia policy? MORE (R-Tenn.) said Sunday. [WATCH VIDEO]

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"We understand some people are going to get arms that should not be getting arms," Corker said. 

"But we still should be doing everything we can" to support rebel forces battling to overthrow embattled Syrian President Bashar Assad, Corker added during an appearance on CBS's "Face The Nation."

As the top Republican on the Senate Foreign Relations Committee, Corker has been one of the Senate's most vocal backers of U.S. military support for Syria's rebels.

Earlier this month, Corker was one of 10 members of a Foreign Relations panel to vote for American military intervention in Syria.

The White House was poised to begin targeted attacks inside Syria in retaliation for Assad's reported use of chemical weapons against rebel positions near Damascus.

But those strikes are now on hold indefinitely, as Washington and Moscow pursue a disarmament plan for Syria.

Secretary of State John KerryJohn Forbes KerrySeinfeld's Jason Alexander compares Trump dance video to iconic Elaine dance This time, for Democrats, Catholics matter President's job approval is surest sign Trump will lose reelection MORE and Russian Foreign Minister Sergei Lavrov agreed to the plan, which requires Assad to hand over his chemical stockpiles to United Nations oversight.

"I think the opposition views this agreement as a setback," Corker said Sunday, regarding the U.S.-Russia deal.

"But the way to counter that, I think, is to much more strongly equip and train the opposition there on the ground," the Tennessee Republican said.

While the White House has put direct strikes against Syria on ice, Washington has begun directly supplying weapons and equipment to the rebels.

The weapon supplies, consisting mostly of small arms, ammunition and anti-tank weapons, are being coordinated by the CIA and limited to vetted portions of Syria's rebels.

President Obama approved the weapons program back in July, giving the CIA the green light to begin arming Syrian rebels from clandestine bases in Turkey and Jordan, according to reports at the time.

Top Pentagon leaders, including Defense Secretary Chuck HagelCharles (Chuck) Timothy HagelArmy taps University of Wisconsin to lead research into hybrid vehicles, aircraft While our foes deploy hypersonic weapons, Washington debates about funding Hillicon Valley: Democrats request counterintelligence briefing | New pressure for election funding | Republicans urge retaliation against Chinese hackers MORE and Chairman of the Joint Chiefs of Staff Gen. Martin Dempsey, have pushed back against arming Syria's rebels over concerns of growing extremist influence in the country.

American military leaders estimate that extreme Islamist groups now constitute “more than 50 percent” of the rebel force, “and it’s growing by the day," according to recent news reports.

But it would be "a stretch to assert" that al Qaeda-linked militant groups, like Jabhat al-Nusra, have gained such a large foothold among the Syrian rebels, Pentagon press secretary George Little said Friday.

That said, the department stands behind Kerry's assessment that the number of extremists within the rebel forces remains at less than 20 percent, Little told reporters at the Pentagon.

That total, Little added, included all Islamic militant groups fighting alongside anti-government rebels in the country and not just those affiliated with al Qaeda.

U.S. intelligence officials "have a very good handle on who to support and who not to support," Corker said Sunday.

That said, "there's going to be mistakes," Corker added.