Los Cabos, Mexico (CNN) -- President Barack Obama said Monday that he and Russian President Vladimir Putin discussed the conflict in Syria and "agreed that we need to see a cessation of the violence, that a political process has to be created to prevent civil war."

In comments to reporters after almost two hours of talks, Obama said he and Putin had "candid, thoughtful and through conversation" about various issues including Syria and Iran.

On Syria, Obama said he and Putin "pledged to work with other international actors including the United Nations" and its special envoy, former U.N. Secretary-General Kofi Annan.

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Russia vetoed a U.N. resolution on Syria pushed by the United States and other allies, and Moscow is accused of providing military aid to Syrian President Bashar al-Assad's government. The Obama administration says al-Assad's days are numbered and a transition should be worked out to allow the Syrian people to choose their leaders.

Putin said the two leaders were "able to find many commonalities pertaining to all of those issues," but provided no details.

The meeting on the sidelines of the G-20 Summit in Los Cabos, Mexico, was the first time Obama and Putin held face-to-face talks since Putin returned to the president's office earlier this year. The U.S. ambassador to Russia, Mike McFaul, described the leaders as "very businesslike, cordial."

McFaul told reporters about a third of the session was devoted to Syria, making it the biggest single topic. "The fact that the meeting went for two hours, that was because they were talking about Syria and they didn't want to stop talking about Syria," he said. "Both leaders, really, on both sides, wanted to make sure the other side of the table understood the true motivations for what they're trying to do and what they're trying not to do."

Putin thanked the United States for helping Russia join the World Trade Organization last December. Obama later said he would work with Congress to strengthen Russia's trade status with the United States, adding that the two nations will disagree on some issues and must "find constructive ways to manage through any bilateral tensions."

Earlier Monday, veteran Sen. John McCain said the Obama administration "in its desperation" appeared to be placing its hopes for a resolution in Syria on persuading Russia to push al-Assad from power.

"Russia is unlikely to ever support a policy of regime change in Syria," said McCain, R-Arizona, in remarks at the American Enterprise Institute.

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White House National Security Council spokesman Ben Rhodes said Obama reiterated U.S. concerns that continued Russian arms sales to Syria "only perpetuate the conflict" during the meeting in Mexico. He said Putin repeated the Russian position that those sales were part of "longstanding relationships unrelated to the current conflict" -- and he cautioned reporters against reading too much into the terse statement Putin gave afterward.

"When he feels like it was a bad meeting, he'll let you know at some length," Rhodes said.

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