In dueling speeches before the UN General Assembly, Obama branded the Syrian leader a child-killing tyrant while Putin said the world should support Assad against the Islamic State group.
The Russian leader urged UN General Assembly members to unite to fight the jihadist group and warned that he plans to step up support for Assad's forces and has not ruled out air strikes.
The US and Russian presidents clinked glasses and shook hands at lunch with UN Secretary-General Ban Ki-moon after their addresses, but nothing could disguise the gulf in their positions.
Putin and Obama later met for 90 minutes for talks the Russian leader dubbed "constructive and business-likes" and a senior US official called a "business-like back and forth."
Putin appeared pleased that Obama had agreed to Russia having a role in the debate, and said: "In my opinion there is a basis to work on shared problems together."
Both leaders agreed there should be a process of political transition in Syria but, the US official added, they "fundamentally disagreed" on the role of Assad.
"I think the Russians certainly understood the importance of there being a political resolution in Syria and there being a process that pursues a political resolution," the official said.
"We have a difference about what the outcome of that process would be," he added.
In his first speech to the world body in a decade, Putin warned it was an "enormous mistake to not cooperate with the Syrian group which is fighting the terrorists face-to-face."
"We must address the problems that we are all facing and create a broad anti-terror coalition," he declared, proposing a Security Council resolution on a coalition to include Assad and Iran.
Obama said Washington was ready to work with Russia and even Iran against the Islamic State jihadists, but warned this must not mean keeping Assad in power in Damascus indefinitely.
"The United States is prepared to work with any nation, including Russia and Iran, to resolve the conflict," he said.
Rather than a bulwark against jihadist extremism, Obama argued, Assad drives Syrians into the arms of such groups by such acts as dropping "barrel bombs to massacre innocent children."
Not to be outdone, the Russian leader blamed the rise of violent extremism on the US military interventions in Iraq and Libya, which he said unleashed chaos in the Middle East.
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