Sen. Dianne Feinstein (D-Calif.) on Monday became the first senior lawmaker to voice support for a Russian proposal for Syria to give control over its chemical weapons to international monitors.

Senator Dianne Feinstein works on Capitol Hill on Thursday June 20, 2013. She meets with Senator Alexander, the ranking member on the Appropriations Subcommittee on Energy and Water Development, of which Senator Feinstein is chairman. They are pictured in Feinstein's office. (Photo by Sarah L. Voisin/The Washington Post) Senator Dianne Feinstein . (Photo by Sarah L. Voisin/The Washington Post)

“I think it’s a very important proposal and I think it needs to get followed up very quickly,” she told reporters Monday afternoon after reading news reports about it.

She noted that United Nations General Secretary Ban Ki-Moon and British Prime Minister David Cameron have already signaled support for the plan and suggested American officials should also take it under consideration.

“I think if the U.N. would accept the responsibility of maintaining these [chemical weapons] facilities, seeing that they’re secure and that Syria would announce that it is giving up any chemical weapons programs or delivery system vehicles that may have been armed, then I think we’ve got something,” she said.

Administration officials said Monday that they would review the proposal.

“We would have to take a hard look," deputy national security adviser Ben Rhodes said on MSNBC. "Any transfer of chemical weapons to international control would be a positive development."

Another deputy national security adviser, Tony Blinken, said the Obama administration “would welcome a decision and action by Syria to give up its chemical weapons."

But Blinken also expressed doubt that Syria would follow through.

A State Department official, Marie Harf, said the proposal was being treated with "serious skepticism."