A Senate debate will begin next week, with a first full Senate vote possible on Wednesday.
The Senate Foreign Relations Committee narrowly approved on Wednesday an authorization that prohibits the use of U.S. combat troops on the ground in Syria and limits the duration of the action to 60 days, with one possible 30-day extension.
Obama said he is striving to convince lawmakers the response in Syria will be limited "both in time and in scope" but still meaningful enough to degrade Assad's capacity to deliver chemical weapons and deter their use.
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"What we're describing here would be limited and proportionate and designed to address this problem of chemical weapons use," Obama said. "And that is going to be the case that I try to make, not just to Congress, but to the American people over the coming days."
Obama also has had trouble rallying international support for a military response to the August 21 chemical weapons attack on Syrian civilians. The British Parliament voted last week against Britain's participation in the action.
Obama said that most leaders of the G-20 countries agreed that Assad was responsible for using poison gas on civilians, although there was disagreement about whether force could be used without going through the United Nations.
He said he did not believe U.N. Security Council support was required.
"Given Security Council paralysis on this issue, if we are serious about upholding a ban on chemical weapons use, then an international response is required, and that will not come through Security Council action," he said.
U.S. Ambassador to the United Nations Samantha Power said on Friday that Assad had barely dented his stockpile of chemical weapons in last month's attack near Damascus, and that Assad knew Russia would back him in the controversy over chemical weapons.
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"We have exhausted the alternatives" to military action, she said at the Center for American Progress think tank in Washington.
Obama declined to say whether he will proceed with military action against Syria if U.S. lawmakers vote against his plan, despite earlier comments from a top aide suggesting he would not use such force without congressional support.
"The president of course has the authority to act, but it's neither his desire nor his intention to use that authority absent Congress backing him," deputy national security adviser Tony Blinken told National Public Radio on Friday.
Obama rejected criticism that he was playing politics by asking Congress for authorization, and acknowledged that Syria's use of chemical weapons was not a direct threat to the United States.
"I did not put this before Congress, you know, just as a political ploy or as symbolism. I put it before Congress because I could not honestly claim that the threat posed by Assad's use of chemical weapons on innocent civilians and women and children posed an imminent, direct threat to the United States," Obama told reporters.
"In that situation, obviously, I don't worry about Congress; we do what we have to do to keep the American people safe," he said.