(CNN) -- It's a stunning turn of events that could change everything on Syria.
Facing the threat of a U.S. military strike, the country's leaders Tuesday reportedly accepted a Russian proposal to turn over its chemical weapons.
The development, reported by Syrian state television and Russia's Interfax news agency, came a day after the idea bubbled up in the wake of what appeared to be a gaffe by U.S. Secretary of State John Kerry.
It quickly changed the debate in Washington from "Should the U.S. attack?" to "Is there a diplomatic way out of this mess?"
Syrian Foreign Minister Foreign Minister Walid Moallem said Tuesday his country had agreed to the Russian proposal after what Interfax quoted him as calling "a very fruitful round of talks" with Russian Foreign Minister Sergey Lavrov on Monday.
Details of such a transfer have yet to be worked out, such as where the arms would go, who would safeguard them and how the world could be sure Syria had handed over its entire stockpile of chemical weapons.
The United States, France, Great Britain and other nations suspect the Syrian government of using chemical weapons repeatedly in its two-year-old civil war -- including an August 21 incident that U.S. officials say killed more than 1,400 people. Syrian officials have blamed rebel forces.
Despite the lack of details, the Russian idea was still gaining traction. 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 would go to the U.N. Security Council on Tuesday with a proposal for Syria to hand over its chemical weapons, but said France -- whose president has already expressed a willingness to punish Syria over its alleged use of the arms -- 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 told CNN's "New Day." "But the fact is, you can't pass up this opportunity -- if it is one."
He said he is working with other senators to write an amendment to the administration's proposed use-of-force resolution that would allow for such a transfer and set out "guidelines, (a) reporting process and benchmarks that have to be met."
Lavrov said Tuesday that Russia's working on a "workable, clear, specific plan" and said it would be presented soon.
A senior administration official involved in Syria policy told CNN that U.S. officials are talking with France and others about how the proposal could be quickly advanced, and to find ways to determine whether Russia and Syria are serious about the idea.
"There are a lot of good questions and there is understandable skepticism," the official told CNN's John King. "But today is better than yesterday. We would rather have a situation where it is possible there is a diplomatic solution in the offing than one with no choice but to pursue military action."
The idea first surfaced 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 Lavrov quickly seized on the comment, suggesting publicly that it would be a way to avoid a U.S. strike on Syria.
Administration officials at first batted down the proposal.
A U.S. official who declined to be identified by name said Monday afternoon that no one in the administration was taking the proposal seriously.
But before long, deputy State Department spokeswoman Marie Harf was saying the United States would take a "hard look" at the idea. White House spokesman Jay Carney said administration officials were "highly skeptical," but had to take a look.
By Monday night, in an interview with CNN's Wolf Blitzer, Obama was calling the idea a "potentially positive development."
"We're going to run this to ground," Obama said. He said the United States will work "to see if we can arrive at something that is enforceable and serious."
But, he said, the idea could simply be a stalling tactic, and Obama said he will 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 and Karla Crosswhite contributed to this report.