(CNN) -- As a Russian proposal to strip Syria of its chemical weapons began to take shape, the White House eased off the gas Tuesday in its drive for congressional approval to strike the Middle Eastern country.
President Barack Obama asked Senate Democrats to delay voting on authorizing military action in Syria while the diplomatic process works itself out, according to senators in the meeting. The president "asked for some time to work things out -- a matter of days into next week," Sen. Dick Durbin said.
Senate Majority Leader Harry Reid said the body's schedule was driven by developments and not by an artificial timeline.
"It's important that we do this well, not quickly," he said. "We'll see what's going on. You know, the last 24 hours has had some remarkable changes in what people are talking about. Let's see what else happens."
And Russia withdrew its request for an emergency United Nations Security Council meeting on the Syrian crisis that had been set for later Tuesday afternoon, a U.N. diplomat said.
Russia -- which has been a key player in efforts to have Syria give up its chemical weapons -- dropped its request due to "changing circumstances," according to the diplomat.
Syria said it is willing to join the Chemical Weapons Convention, Foreign Minister Walid Moallem said in a statement before departing Moscow, according to Russian news agency Interfax.
Earlier Tuesday, Russia's Foreign Ministry said it deemed as "unacceptable" a French proposal -- also backed by some U.S. lawmakers -- asking the Security Council to declare Syria responsible for an August 21 chemical attack that U.S. official says killed more than 1,400 people.
According to Syrian state TV, Syria on Tuesday accepted Russia's proposal to put its chemical weapons under international control, a day after Secretary of State John Kerry floated the idea in what appeared to be an off-the-cuff comment suggesting it would be the only way for Syria to avoid a punishing Western military strike.
Moallem said the country was ready to disclose the location of its chemical weapons, halt production and show facilities to representatives of Russia, the United Nations and other states, according to the Russian Interfax news agency.
Russian Foreign Minister Sergey Lavrov said Tuesday that Russia is working on a "workable, clear, specific plan" and said it would be presented soon.
Speaking to the House Armed Services Committee on Tuesday, Kerry said the United States would look forward to the Russian plan but will demand that it be brought forward and implemented quickly.
"We're waiting for that proposal, but we're not waiting for long," he said.
And despite the apparently reduced urgency from the White House, congressional allies said Congress needs to back up the diplomats with a show of force.
"We're going to continue to work on moving forward with this but keeping pronounced, and I pronounce it now, the credible threat of our doing something about this attack is going to remain," Reid said.
Lavrov told his French counterpart Tuesday that his country wouldn't stand for any resolution blaming the Syrian regime for the use of chemical weapons. Syria is a longtime Russian ally, and Russian officials have argued, as have Syrian officials, that rebel forces could have staged the attack.
France is proposing to make such a request, as are some U.S. lawmakers who are working to draft an alternative resolution that would call for a U.N. resolution blaming the attack on the Syrian government and set a deadline for it to hand over its chemical weapons.
Otherwise, the draft U.S. Senate proposal would authorize use of military force punishing Syria.
Moallem said earlier Tuesday that his country had agreed to the Russian proposal after what Interfax quoted him as calling "a very fruitful round of talks" with his Russian counterpart, Lavrov, on Monday.
Despite the lack of details, the idea was gaining traction around the world. On Monday, U.N. Secretary-General Ban Ki-moon expressed support for the concept. Tuesday, a Chinese Foreign Ministry spokesman said it would safeguard stability in the region. Syrian ally Iran welcomed the proposal, and Germany expressed interest.
French Foreign Minister Laurent Fabius said France will not accept delays in the transfer.
"We need quick results," Fabius said.
European Union Foreign Affairs Secretary Catherine Ashton said she supported the French plan to bring the issue to the Security Council, saying the proposal "now needs to be fully worked up as quickly as possible."
Even Sen. John McCain, R-Arizona, a proponent of a military strike on Syria, said the idea was worth exploring.
"I'm very, very skeptical," he said on CNN's "New Day." "But the fact is, you can't pass up this opportunity -- if it is one."
McCain is one of the key players crafting the Senate resolution, which would be an alternative to the use-of-force resolution proposed by the administration. It would allow the president to deploy U.S. forces against Syria if the United Nations doesn't pass a resolution that condemns the attack, says it was "committed by the Syrian regime" and sets a deadline to hand over the weapons.
The senators have not decided whether the resolution would include limits on the use of U.S. force, such as sending troops to the country.
The Russian proposal surfaced publicly Monday, when Kerry -- responding to a reporter asking what Syria could do to stop a U.S. attack -- suggested that Syrian President Bashar al-Assad "could turn over every single bit of his chemical weapons to the international community in the next week."
"He isn't about to do it, and it can't be done, obviously," Kerry added.
His spokeswoman, Jen Psaki, sought to roll back the comments, saying the secretary was simply responding to a "hypothetical."
But it turns out Russian President Vladimir Putin brought the idea up to Obama last week, a senior administration official said Monday night. Kerry and Lavrov have also been discussing ways for Moscow to get involved for more than a year, the official said. But U.S. officials didn't realize how serious Russia was until Lavrov seized on Kerry's comment on Monday, the official said.
Monday night, in an interview with CNN's Wolf Blitzer, Obama called the idea a "potentially positive development."
But he also said the idea could simply be a stalling tactic, and said he would continue to press his case for military action. He is scheduled to address the nation Tuesday night.
"If we can accomplish this limited goal without taking military action, that would be my preference," Obama said Monday. "On the other hand, if we don't maintain and move forward without a credible threat of military pressure, I don't think we'll actually get the kind of agreement I'd like to see."
The opposition Free Syrian Army urged the world not to buy into the idea of transferring control of the chemical weapons, which it called a trick.
"Here we go again with the regime trying to buy more time in order to keep on the daily slaughter against our innocent civilians and to fool the world," said Louay al-Mokdad, a spokesman for the group.
CNN's Stephanie Halasz, C.Y. Xu, Yousuf Basil, Ed Payne, Ashley Killough, Tom Cohen, Dana Bash, Steve Brusk, Dan Merica, Paul Steinhauser, Zachary Wolf, Samira Said, Joe Vaccarello and Karla Crosswhite contributed to this report.