At a summit which Putin is hosting in a tsarist palace outside St. Petersburg, the Group of 20 developed and developing economies will try to forge a united front on growth, trade, banking transparency and fighting tax evasion.
The club that accounts for two-thirds of the world's population and 90% of its output is divided over issues such as emerging market turmoil and the Federal Reserve's decision to end its programme of stimulus for the US economy.
But no rift is wider than the one between Obama and Putin over possible military intervention in Syria, and both presidents turned up the volume on Wednesday.
Obama used a visit to Sweden to build his case for a military response to the "barbarism" of a chemical weapons attack on Aug. 21 which Washington blames on Syrian forces loyal to President Bashar al-Assad.
Obama, who is seeking approval for military strikes from Congress, said: "My credibility is not on the line. The international community's credibility is on the line.
"And America and Congress' credibility is on the line, because (otherwise) we give lip service to the notion that these international norms are important."
Putin said Congressional approval without a UN Security Council resolution would be an act of aggression, and accused Secretary of State John Kerry of lying by playing down the role of the militant group al Qaeda with rebel forces.
"Our opponents' arguments are very weak. To be honest, they are non-existent," Putin said in Moscow.
Putin's comments dimmed prospects of a compromise which had been raised when he said in an interview he did not rule out supporting military action - if it was approved by the UN Security Council and there was proof Assad's forces had resorted to chemical warfare.
Foreign ministers from key states in the G20 - which includes all five permanent Security Council members - will discuss Syria on the sidelines of the meeting although it is not formally on the summit agenda.
The G20 lacks the powers of the Security Council, but Putin would like to see a consensus to avert military action in what would be a significant - but unlikely - diplomatic triumph for Russia, Syria's key arms supplier and international ally.
Lack Of Harmony
The G20 achieved unprecedented cooperation between developed and emerging nations to stave off economic collapse during the 2009 financial crisis, but the harmony has now gone.
There are likely to be some agreements - including on measures to fight tax evasion by multinational companies - at the summit in the spectacular seafront Peterhof palace complex built on the orders of Tsar Peter the Great.
An initiative will be presented to leaders on refining regulation of the $630 trillion global market for financial derivatives - such as futures, options and swaps - to prevent a possible markets blow-up.
Steps to give the so-called 'shadow banking' sector until 2015 to comply with new global rules will also be discussed. But consensus is proving hard to achieve among developed economies as the United States takes aggressive action to spur demand and Europe moves more slowly to let go of austerity.
Meanwhile, emerging economies in the Brics - Brazil, Russia, China and South Africa - are divided over the role of the US dollar in the world economy.
And there has been no sign of them rallying behind the fifth Brics member, India, after it called last Friday for joint currency intervention.
The International Monetary Fund will call at the meeting for strengthened global action to revitalise growth and better manage risks, an IMF document obtained by Reuters showed. Advanced economies led by the United States will increasingly drive global growth while emerging countries are at risk of slowing, due to tighter US monetary policy, it said.
"The greatest worry may well be a prolonged period of sluggish global growth," the IMF said.
But with the United States and other advanced economies picking up speed, the IMF said it still expected global growth to accelerate in 2014 from this year, helped by the highly accommodative monetary conditions in the rich world.
Former Russian finance minister Alexei Kudrin also urged caution, warning of the threat posed by debt and suggesting the main problems of the global financial crisis may not have been overcome yet.
"We aren't in a recovery - we have just won a breathing space," he said.
Further friction on the fringes of the summit could be caused by Obama's plans to meet human rights activists including members of a gay rights group which staged protests against a law Putin signed banning "gay propaganda" among minors.
The law has been widely criticised in the West and is one of the areas on which Russia and the United States have fallen out as relations deteriorated this year and Obama pulled out of a meeting with Putin that would have been held on Wednesday.