President Obama

President Obama walks to the Oval Office on Tuesday. (Win McNamee/Getty Images / MCT / September 10, 2013)

WASHINGTON -- President Obama and his French and British counterparts have agreed to work with Russia and China to "run to ground" a new proposal to put Syrian chemical weapons under international control, a senior administration official said Tuesday.

In separate morning phone calls between Obama and French President Francois Hollande and British Prime Minister David Cameron, the leaders agreed to explore the viability of the new proposal floated by Russian officials on Monday.

An advisor to Obama said the administration is interested in the idea of a diplomatic solution under which the Syrian government would turn over all chemical weapons in order to avert U.S. military strikes. Obama is contemplating punitive action in response to an alleged chemical attack in the Damascus suburbs last month.

The White House looks at the remainder of this week as a critical period for determining whether the proposal is a serious one.

The efforts to check out the proposal will begin Tuesday at the United Nations, according to the White House, and include a discussion on how to put together a potential U.N. Security Council resolution.

France -- among the most vocal supporters of an armed reprisal against Assad’s government -- said Tuesday that it would introduce such a resolution.

Obama's calls with allies came in advance of midday trips to speak with lawmakers on Capitol Hill.

Obama's speechwriters will be putting the final touches on his scheduled address to the nation Tuesday night, expected to last 15 minutes or so in the East Room of the White House.

Some of the details of the address will depend on how talks go with lawmakers Tuesday, an official said, and on what the initial tests of the Russian proposal turn up.

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Twitter: @cparsons 

christi.parsons@latimes.com