Barack Obama said "he was elected to end wars not start them" but added that failing to respond to the chemical weapon attack in Syria would send out the wrong message.
The US President said he would "greatly prefer to work through the United Nations to get this done."
US President Barack Obama said a "majority" of world leaders believe that Bashar-al Assad's regime used chemical weapons.
He added that it was "unanimous" among the leaders that chemical weapons were used in the country.
US President Barack Obama said the alleged use of chemical weapons by Bashar al-Assad's regime is "not just a Syrian tragedy, it's a threat to global peace and security."
If the West waits for a UN resolution until intervening in Syria, Britain would be "contracting out our foreign policy, our morality, to the potential of a Russian veto," David Cameron said in response to a question from ITV News deputy political editor Chris Ship.
"I think that is a very misguided approach," he said, describing last night's debate as "frustrating."
David Cameron said because there was never going to be an agreement on military action at the G20 summit, Britain decided to focus its effort on securing more humanitarian aid for the crisis in Syria.
He said the the case made by those countries who believed there was a need to make a stand was "extremely powerful."
He reiterated that Britain will not be part of any military action.
Russian president Vladimir Putin has said he is concerned about the effect of the Syrian conflict on the world economy.
He said video evidence of alleged chemical attacks in Syria was "provocation by the militants who expect to get help [from the West]."
He added that surveys had shown that people in the US and other Western countries were against military intervention in Syria.
US president Barack Obama and Russian president Vladimir Putin met for 20 minutes on the sidelines of a G20 summit today but remained at odds over the conflict in Syria, Putin's senior foreign policy adviser said.
"They sat down before today's working session, in armchairs, and had a 20-minute chat, one on one," the adviser, Yuri Ushakov, told Reuters.
He said Syria was the main topic and said: "No, their (positions) have not come closer."
The G20 summit leaders' declaration has been published and its 27 pages feature no mentions of Syria.
The US State Department said it had evacuated non-emergency personnel and family members from its embassy in the Lebanese capital Beirut, as Congress debates a military strike on neighbouring Syria.
"The Department of State drew down non-emergency personnel and family members from Embassy Beirut due to threats to US Mission facilities and personnel," a statement on the Beirut embassy's website said.
The UN Syrian peace envoy Lakhdar Brahimi says no country can take the law into its own hands and there must be Security Council approval before any military action is undertaken.