The US and France insisted Syria's President Bashar al-Assad must go, but Russia said it would be an "enormous mistake" not to work with him to tackle Islamic State (IS) militants.
The US and Russia hinted at compromise.
Barack Obama said he would work with any nation, and Vladimir Putin called for a "broad coalition".
The pair will meet in New York later.
In his speech, Mr Obama said compromise among powers would be essential to ending the Syrian conflict, which has claimed more than 200,000 lives and forced four million to flee abroad.
"Lasting stability can only take hold when the people of Syria forge an agreement to live together peacefully," he said.
"The US is prepared to work with any nation, including Russia and Iran, to resolve the conflict. But we must recognise that there cannot be, after so much bloodshed, so much carnage, a return to the pre-war status quo."
Speaking soon after, Mr Putin said it was an "enormous mistake to refuse to cooperate with the Syrian government and its armed forces who are valiantly fighting terrorism face-to-face".
He also called for the creation of a "broad anti-terror coalition" to fight IS, comparing it to the international forces that fought against Nazi Germany in World War Two. (+ videos) » | Monday, September 28, 2015
