Putin, an ally of Syria and President Bashar Assad, is a reminder of resistance to U.S. pleas for Moscow to intervene after a deadly chemical weapons attack last month in the Damascus suburbs. The Obama administration says more than 1,400 people were killed. Other estimates are lower, and the Syrian government denies responsibility, saying opposition rebels were to blame.
Obama and Putin shared a 15-second greeting and may talk on the sidelines of the summit.
Ben Rhodes, Obama's deputy national security adviser, told reporters that the president was making calls to members of Congress while he attends the two-day economic summit.
In Washington, the administration turned its attention to the opposition Republican-controlled House of Representatives after the Senate Foreign Relations Committee voted 10-7 Wednesday to authorize the ``limited and specified use'' of armed forces against Syria. It voted to support a resolution that restricts U.S. military action to 90 days and bars ground troops from combat.
The vote marked the first formal response in Congress, four days after Obama surprised the world by putting off an anticipated cruise missile strike against Syria and instead asked lawmakers to unite behind such a plan.
The administration's plan for military action in Syria needs approval from committees in both chambers and then approval from both full chambers to go ahead. The measure is expected to reach the Senate floor next week. The timing in the House is more uncertain.
But Obama on Wednesday, asked whether he would take action if he fails to get approval from Congress, told reporters in Sweden that as commander in chief, ``I always preserve the right and the responsibility to act on behalf of America's national security.''
Secretary of State John Kerry, testifying before Congress, insisted Wednesday that the U.S. military response would be restricted as Americans fatigued by more than a decade of war in Iraq and Afghanistan show little interest in getting involved in Syria.
"I don't believe we're going to war, I just don't believe that,'' Kerry told the House Foreign Affairs Committee.
Kerry told the committee that he believed Obama would address the nation on Syria in the next few days. The president returns home Friday night.
Few, if any, members of Congress dispute the Obama administration's claim that Assad was responsible for the chemical weapons attack.
But many Republicans and Democrats in the House question why the U.S. should get involved now in a Syrian civil war that has killed an estimated 100,000, displaced millions and is in its third year. The chamber's most powerful Republicans, House Speaker John Boehner and Majority Leader Eric Cantor, have expressed support for military action, but others in their party remain reluctant or opposed.
Days from a vote, an Associated Press survey of senators found 34 of its 100 members supporting or leaning toward military action, 26 opposed or leaning against and 40 undecided.