Vladimir Chizhov, Russia's emissary to the European Union, said the plan calls for Syria's chemical weapons to be placed under international supervision -- inside that country initially, at least.
"The ultimate aim is to have these weapons destroyed," Chizhov told CNN's Christiane Amanpour.
He acknowledged the task of gaining control of the weapons and destroying them with a civil war raging in Syria won't be easy, voicing worries about what rebel fighters might do.
Separately, the United States, France, and Britain discussed a U.N. Security Council draft resolution, according to a spokesman for British Prime Minister David Cameron.
How long will window be open?
Ambassadors from the U.N. Security Council's five permanent members -- the United States, Russia, China, Britain and France -- met the same day for less than an hour, a diplomat with knowledge of the meeting said.
While the focus now is on Switzerland, U.N. headquarters in New York is expected to become the focal point early next week when U.N. chemical weapons inspectors deliver their report to the Security Council -- as early as Monday or Tuesday, sources say -- on the August 21 attack in Syria.
In Washington, the debate about what the United States should do in Syria is not over. While Obama has said he wants to give the diplomatic process a chance, he hasn't said how long he'll wait before possibly pushing again for military action.
After his meeting earlier this week with Senate Democrats, Sen. Dick Durbin said the president asked lawmakers "for some time to work things out -- a matter of days into next week." Another Senate Democrat, though, said it could take weeks to determine if diplomatic efforts will pan out.
Members of Congress will watch Kerry's trip closely for a sense of Obama's next move after weeks of beating the drum for military action against Syria.
"If diplomacy fails, he's painted himself into a corner," Sen. Lindsey Graham said after Obama's speech. "The leader of the free world can't say all these things at the end of the day and do nothing."
Senior State Department officials have cautioned that negotiations over the proposed deal may not conclude after the scheduled round of talks in Geneva. The plan would be to take any final deal to the U.N. Security Council to be formalized in a resolution.
Outcome far from certain
While that process unfolds -- if it does successfully -- Obama continued to keep the door open for military action, despite exhortations from Putin that he drop any hint of a threat.
The U.S. president has said any military operation in Syria would be targeted, limited and not involve U.S. ground forces. Its goal would be to degrade al-Assad's ability to use chemical weapons.
Obama has also said any strike would be effective -- saying Tuesday that "the United States military doesn't do pinpricks" -- and he has ordered armed forces to be poised in the region "to keep the pressure on Assad."
U.S.-funded (if not U.S.-made) weapons began flowing to Syrian rebels about two weeks ago, a U.S. official said. Coordinated by the CIA, the supplies include light weapons, ammunition and anti-tank weapons in addition to nonlethal aid the United States has long been providing.
A big question looming over the diplomatic talks is whether any U.N. resolution includes a potential for military action should al-Assad not cooperate. That's something the United States and its allies have favored, while Putin has said his country could veto any measure there that contains such a threat.
Analysts say Kerry, as leader of the U.S. diplomatic efforts, has his work cut out for him.
"I think it's unlikely the Russian government is going to relent on this issue of whether or not it would support the use of force in a security council resolution," said Nicholas Burns, a former senior State Department official now at Harvard University's Kennedy School of Government.
"They've been consistent since day one of the Syrian crisis that they did not want to see the United States or anyone else use force. I think that's one of the ambitions the Russians have going into this negotiation in Geneva," he added.
Former Secretary of State Madeleine Albright said in an exclusive interview on CNN's "The Lead with Jake Tapper" that Kerry must not take the threat of force off the table in his talks with the Russians even if they insist he drop it.
"This is the way that diplomacy works. You use the threat of the use of force to get some action in diplomacy, and then diplomacy just to figure out what you do about the threat of the use of force," said Albright, who served as America's top diplomat under President Bill Clinton.
"One of the things I know from trying to get Security Council resolutions is that they take a while," said Albright. "But my personal feeling here is that it is that threat of the use of force, and the president made very clear that our ships would stay in the area, and that the use of force would stay on the table."