The awkward initial encounter came after some other leaders arriving in St Petersburg pointedly sided with Russia in its opposition to US-led military action.
Intervention would damage the global economy by pushing up oil prices, China said.
Syria is not a significant oil exporter, but the prospect of conflict in the Middle East often pushes up oil prices.
"Military action would have a negative impact on the global economy, especially on the oil price - it will cause a hike in the oil price," said Zhu Guangyao, the Chinese Vice-Finance Minister.
Brazil, India and South Africa also worry that intervention would do economic harm, according to Putin's officials.
Dmitry Peskov, a spokesman for the Russian President, said the leaders of the large emerging economies spoke before the St Petersburg summit and agreed that Syrian intervention would have an "extremely negative effect" on the global economy.
While the British and French governments have both backed the principle of military intervention to punish the Assad regime's alleged use of chemical weapons, the European Union as a whole is opposed, European officials said.
Herman van Rompuy, the EU President, arrived at the summit with a warning against military action.
"There is no military solution to the Syrian conflict," he said. "Only a political solution can end the terrible bloodshed, grave violations of human rights and the far-reaching destruction of Syria."
Before the summit began, the Pope also cautioned against intervention, urging all leaders in St Petersburg to end "the futile pursuit of a military solution".
Iran, Syria's strongest regional ally, also repeated its fierce opposition to intervention.
Ayatollah Ali Khamenei, Iran's supreme leader, warned that the US will "suffer loss" if it launches a military intervention in Syria.
Tehran is supporting the Assad regime through its Hizbollah militia allies.
The US is using alleged chemical weapons use as a pretext to strike Syria, Khamenei said in a speech in Tehran, the Iranian leadership's latest criticism of Obama's position.
Earlier this week, a leader of Iran's Republican Guard suggested that Iran would resist US intervention in Syria "until the very end".
The growing signs of opposition left Obama with few effective allies in St Petersburg.
After the House of Commons last week voted against British involvement in any strikes, Francois Hollande of France is the last world leader still willing and able to support US action with military force.
Hollande insisted that it was necessary to punish the Assad regime over the chemical incident, since only such punishment would cause Damascus to agree to a peaceful outcome to the civil war.
"Punishment will allow negotiation, but obviously it will be difficult," Hollande said.
The Commons vote has left British PM David Cameron largely powerless and able to provide only moral support for any intervention.
Cameron and Obama will not hold a formal meeting in St Petersburg, but Cameron used television interviews on his arrival in Russia to once again urge Obama to strike.
Obama has said that using chemical weapons would be a "red line" for intervention, Cameron pointed out.
"I absolutely believe that having set a red line on the further big use of chemical weapons, I think it would be wrong if America was to step back and having set that red line to do nothing," he said. "I think that would send an appalling signal to President Assad."
Conservative MPs have suggested the vote last week could harm US-UK relations, but Cameron insisted transatlantic ties remain as strong as ever.
