The two leaders met on the sidelines of the UN General Assembly in New York on Monday in a meeting which lasted 90 minutes.
A senior US official described the meeting as "business-like back and forth," while Putin called it "constructive and business-likes" and said the discussion was "very constructive and surprisingly open."
"In my opinion there is a basis to work on shared problems together," but “disputes remain," Putin told reporters following the meeting.
"We have a lot in common," he said, adding "we have sound grounds to work on the points of concern together."
The US official said the two leaders decided that conversations between the American and Russian military officials should continue over the crisis in Syria, but added that Obama and Putin "fundamentally disagreed" on the role of Assad in Syria.
"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.
However, "we have a difference about what the outcome of that process would be," he added.
Before the meeting, both Obama and Putin delivered speeches to the United Nations General Assembly, during which the two leaders expressed completely different views on Assad.
Putin said Assad is the only option in campaign against the Daesh (ISIL) terrorists, noting he is “valiantly fighting terrorism face to face."
As part of a plan to fight against Daesh Takfiri terrorists, Russia has been beefing up its military presence in Syria, equipping Damascus with advanced military aircraft such as the Mikoyan MiG-31 fighter jets and other sophisticated equipment.
Putin has said that Russia's support for the Assad government was in accordance with the UN Charter, since "we have been providing assistance to legitimate government entities only."
Moscow’s military support for Assad, however, goes against the current US policy, which calls for the Syrian president’s ouster.
Syria has been gripped by deadly violence since March 2011. According to reports, the United States and its regional allies - especially Qatar, Saudi Arabia and Turkey - have been supporting the militants operating inside Syria since the beginning of the crisis; Press TV reported.