"I think you have to take it with a grain of salt initially," he told "NBC Nightly News" in an interview. "This represents a potentially positive development," he said, adding that Secretary of State John Kerry would explore with Russia how serious the offer is.
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Secretary of State John Kerry suggested earlier Monday that Syria could avoid a potential US air attack by putting its chemical weapons under international control. Syria's ally Russia quickly took the idea to Syria's foreign minister, who said Damascus welcomes the proposal.
Obama was speaking in one of six television interviews he gave on Monday to make his case that Congress should grant him authority to take action against Syria in response to an alleged Aug. 21 chemical weapons attack that killed more than 1,400 people.
He also said he hasn't decided whether he would launch a military strike on his own if Congress votes down the resolution. He says he is taking the vote and what the American people are saying "very seriously."
The president added he knew there was a risk in asking Congress to approve a military strike, but that he was confident that lawmakers were taking the issue seriously and "doing their homework."
The White House is making an all out effort to win congressional support for a limited military strike against Syria, holding numerous briefings for lawmakers. The president plans to address the nation on television Tuesday night and is due to speak to senators of both parties on Capitol Hill during the day.
Obama told CNN that any diplomatic effort must be serious.
"And we don't want just a stalling or delaying tactic to put off the pressure that we have ... right now," he said.
"We have to maintain this pressure, which is why I'll still be speaking to the nation tomorrow about why I think this is so important," he added.
The president said a breakthrough on control of Syrian chemical weapons would not solve "the underlying terrible conflict inside of Syria. But if we can accomplish this limited goal without taking military action, that would be my preference."
Obama said he has not made up his mind whether he will forge ahead with military action if Congress votes his proposal down.
"It's fair to say that I haven't decided," he told NBC.
Obama faces an uphill struggle to win approval from lawmakers, and he acknowledged that he has doubts about how the vote will turn out.
"You know, I wouldn't say I'm confident," he said in his NBC interview.
Regarding ties with Russia, Obama told PBS NewsHour he had discussed a potential diplomatic solution on Syria with Russian President Vladimir Putin last week at the G20 summit.
"I did have those conversations. And this is a continuation of conversations I've had with President Putin for quite some time," Obama said.
The president told CNN that any diplomatic effort must be serious: "We don't want just a stalling or delaying tactic to put off the pressure that we have ... right now," he said.
"We have to maintain this pressure, which is why I'll still be speaking to the nation tomorrow about why I think this is so important," he added.
The US president said a breakthrough on control of Syrian chemical weapons would not solve "the underlying terrible conflict inside of Syria. But if we can accomplish this limited goal without taking military action, that would be my preference."
Reuters, AP contributed to this report
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