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* Obama and Putin meet at G20 summit
* Relations strained by Syria crisis
* Obama later than others for summit dinner
By Matt Spetalnick and Steve Holland
ST. PETERSBURG, Russia, Sept 5 (Reuters) - A brief photo-op on Thursday between Barack Obama and Vladimir Putin spoke volumes, limited mostly to tight smiles and a businesslike handshake between U.S. and Russian leaders bitterly divided by the crisis in Syria.
Their sparse encounter outside a tsarist palace in St. Petersburg at the start of a Group of 20 (G20) economic summit underscored the dismal state of U.S.-Russia relations, with tensions mounting over Obama's threatened military strike against Syria, a Russian ally.
Obama and Putin have never had anything close to personal chemistry, and there was hardly any on display as the armoured limousine carrying the U.S. president pulled up to where Putin waited to greet arriving world leaders.
Both offered thin smiles, exchanged pleasantries and gripped hands for the cameras. Obama could be heard pronouncing the weather or the palace or both "beautiful" and then headed inside alone.
It was the only one-on-one public appearance planned between the leaders in St. Petersburg, after Obama called off a separate Moscow summit in response to Russia's granting of asylum last month to Edward Snowden, a former U.S. spy agency contractor who had exposed secrets of American surveillance programmes.
But Syria was the biggest source of strain in St. Petersburg, where Obama's effort to rally world support for a military strike against Syrian President Bashar al-Assad over suspected chemical weapons use was pitted squarely against Putin's efforts to prevent such action.
The two were expected to talk informally on the summit sidelines but there was little expectation they would narrow their differences.
Obama arrived later than most of his fellow leaders for Thursday's working dinner and, when a reporter shouted a question on whether any progress had been made on Syria, was reported to have said leaders had only discussed the economy so far.
At a news conference in Stockholm on Wednesday, Obama said, "We've kind of hit a wall," when asked what had gone wrong with the "reset" in relations with Russia that he touted as a signature foreign policy accomplishment early in his first term.
Scrutinising body language between the two has become a diplomatic pastime as the two have engaged in some of the most awkward personal encounters of U.S. and Russian leaders since the end of the Cold War.
At a G8 summit in Northern Ireland in June, Putin scowled his way through talks with Obama, who later likened him to a "bored kid in the back of the classroom".
The St. Petersburg summit appeared to be unfolding with similar tensions in play.
A day earlier, Putin bluntly accused U.S. Secretary of State John Kerry of lying by playing down the role of the militant group al Qaeda among Syrian rebel forces.
Then, on the way to the summit, Ben Rhodes, Obama's deputy national security adviser, dismissed as "implausible theories" the notion put forward by Putin that anti-Assad rebels may have been to blame for the Aug. 21 gas attack that killed hundreds of people near Damascus.
In the broadcast part of the first summit session on Thursday, Obama and Putin milled around talking to other leaders but not to one another.
On Friday, Obama plans to meet Russian human rights activists to underline U.S. displeasure over new laws that critics of the Kremlin say clamp down on dissent, violate gay rights and restrain non-governmental organisations.
That is all but certain to be taken by Putin as a swipe at him and meddling in Russia's domestic affairs.