WASHINGTON—With Congress on the verge of considering whether to authorize President Barack Obama to launch a retaliatory attack on Syria, the United States and Russia on Monday embraced a proposal that would allow Syria to avoid a U.S. missile strike by relinquishing control of its chemical weapons.

Obama called the proposal a “significant breakthrough” in an interview with ‘NBC Nightly News,” and he said on PBS’s “NewsHour” that he had discussed the plan with Russian President Vladimir Putin during the Group of 20 summit last week in Russia.

But after two weeks of pressing for the need for a U.S. strike, Obama also said he remains skeptical that Syrian President Bashar Assad would agree to the idea. If he does, Obama told ABC News, he would “absolutely’’ hold off on a military strike.

“This may be a first step in what potentially could be an end to terrible bloodshed and millions of refugees throughout the region that is of deep concern to us and our allies,’’ Obama said on “CBS Evening News.”

The diplomatic advance came as evidence mounted that Obama’s request for congressional approval for a strike remained widely unpopular, both in Congress and with the American people, despite a public push that has included impassioned presentations in recent days by Secretary of State John Kerry, National Security Adviser Susan Rice and United Nations Ambassador Samantha Power. Informal counts found House members who said they planned to vote “no” far outnumbering those willing to say they would vote “yes,” and a new McClatchy/Marist poll of U.S. public opinion showed nearly 3-to-1 opposition among registered voters to military action.

The Senate postponed its vote on a resolution that had been scheduled for Wednesday. Democratic aides said the delay was intended to give the Russian proposal time to come together. “I don’t think we need to see how fast we can do this,’’ Senate Majority Leader Harry Reid, D-Nev., said Monday night. “We have to see how well we can do this.’

The sudden possibility of a diplomatic solution came as Assad launched a public relations campaign of his own, granting an interview to American television, and new information emerged that raised questions about the U.S. version of a chemical weapons attack Aug. 21 in suburbs east of Damascus.

Speaking to interviewer Charlie Rose, Assad denied using chemical weapons and warned that if the U.S. struck Syria, “you should expect everything,” apparently referring not only to potential retaliation from Syrian forces, but also to fallout from his allies Iran and the Lebanese militant group Hezbollah.

Obama said repeatedly that Assad does not have a “credible means to threaten the United States,’’ but he acknowledged that his allies, including Iran and Hezbollah, could engage in terrorist strikes against the U.S.

Assaed also said that the Obama administration hadn’t presented any solid evidence that the regime had used chemical weapons, and he invoked the unpopularity of a strike among Americans, especially without international backing.

“The polls show that the majority now don’t want a war anywhere, not only against Syria,” Assad said. “But the Congress is going to vote about this in a few days. And I think the Congress is elected by the people and represent the people and work for their interests.”

The Obama administration spent much of the afternoon backpedaling on Kerry’s remarks _ insisting they were rhetorical and not intended as an offer _ but by that time the Russians, the Syrians, the British and some members of Congress had welcomed the plan as a detour on the U.S. march toward action.

By the end of the day, the Russian proposal had surfaced in Obama’s six network TV interviews, briefings at the White House and the State Department, and at a White House appearance by former Secretary of State Hillary Clinton was speaking.

White House spokesman Jay Carney made no mention of Obama’s previous conversations with Putin. He said the reason that Russia had made the proposal is because of the “intense pressure” on Assad by the United States. He added that the administration would continue building support in Congress for a limited U.S. strike.

“We would not be having this conversation … if it weren’t for the fact that there is the credible threat of U.S. military action in response to their use of those weapons,” he said.

The twist of events began at a news conference in London, where Kerry said a strike could be avoided if the Assad regime turned over “every single bit” of its chemical arsenal to international authorities by the end of the week.

By the time the State Department clarified that Kerry’s remarks were intended only as rhetoric about a highly improbable scenario, Moscow already had pounced on the opening.

Moscow’s maneuvering to turn Kerry’s ad libs into a potential diplomatic breakthrough only added another obstacle to Obama’s task of selling Congress and the public on an unpopular, ill-defined strike.

As of Monday, the Obama administration had provided classified briefings to 185 lawmakers. Others have attended unclassified briefings or one-on-one meetings. The president will meet with Senate Republicans Tuesday at the Capitol before a prime-time address on television.

Obama said he knows he faces an uphill battle in persuading Americans to support the strikes. He said on PBS that he does not think he will convince the overwhelming majority of the American people that he should take action. Even members of his own family are “suspicious’’ of military intervention, he said. But, Obama said, he believes he can make a “very strong case’’ to the nation.

In his interviews Monday, Obama made it clear that he recognizes that congressional authorization is by no means assured. “I wouldn’t say I’m confident,” he said on NBC.

Obama declined to say whether he would use force in Syria without congressional approval.

“I think it’s fair to say that I haven’t decided,” he told NBC. “I am taking this vote in Congress and what the American people are saying very seriously. I knew by bringing this to Congress that there was a risk that the American people, you know, just could not arrive at a consensus around even a limited strike. Because if you ask somebody, you know, I read polls like everybody else.”

Lawmakers, some of whom are opposed to the strikes, hailed the Russian proposal, which could be just the lifeline they needed from the dilemma of either supporting the administration’s strike plans or siding with constituents who’ve repeatedly rejected U.S. intervention in Syria.

Sen. Richard Durbin, D-Ill., said he saluted any diplomatic “effort to resolve this in a verifiable way and do it with dispatch.”

Sen. Dianne Feinstein, D-Calif., chairman of the Senate Select Intelligence Committee, said she would welcome Syria’s transfer of its chemical weapons to international monitors for destruction, to prevent a military strike.

“I believe that Russia can be most effective in encouraging the Syrian president to stop any use of chemical weapons and place all his chemical munitions, as well as storage facilities, under United Nations control until they can be destroyed.”

Some lawmakers were skeptical.

“How would you know how many chemical weapons they turn over?” said Rep. Lynn Westmorlend, R-Ga., a member of the House Select Intelligence Committee. “This is another ad lib statement someone gave in a speech. It’s just a real cluster right now.”

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