SAN JOSÉ DEL CABO, Mexico — President Obama and his Russian counterpart, Vladimir V. Putin, finally had their face-to-face meeting on Monday, as Mr. Obama pressed Mr. Putin to work with him to ease President Bashar al-Assad of Syria out of power, a move increasingly viewed by the West as the only way to end the bloodshed that has been under way there for more than a year.

But after two full hours together, Mr. Putin was still balking, appearing afterward with Mr. Obama before reporters in a grim tableau that seemed to bespeak the frustration on both sides. During the few minutes that it took their handlers to usher reporters out of the room after their prepared remarks, the two leaders remained seated, side by side, staring straight ahead, with none of the interaction or small talk that leaders usually engage in before the cameras. “We agreed that we need to see a cessation of the violence, that a political process has to be created to prevent civil war,” Mr. Obama said.

During the meeting, American officials said, Mr. Putin spent considerable time pointing to what the Russians view as failed examples of political transition in Egypt and Libya as well as their concern that the West does not have a credible plan for what would happen to Syria’s various battling factions and ethnic groups if Mr. Assad stepped down from power.

Mr. Obama made a long and detailed effort to reassure Mr. Putin that the United States does not want to come between Russia and Syria, a strategic ally that Russia views as its last real bastion of influence in the region, the officials said. The Americans acknowledged that Russian officials have not really believed them when they have made these assurances in the past; Monday’s meeting, they said, provided Mr. Obama the chance to try to make this case personally to Mr. Putin.