The new plan to reduce violence was designed to prevent Syrian forces from bombing American-backed opposition groups while claiming the groups were embedded with Nusra forces, which until recently were officially linked to Al Qaeda.

The situation in Syria on Sunday showed that the cease-fire that began last Monday was fraying. Fighter jets fired at least four missiles at opposition neighborhoods in Aleppo, Syria’s largest city, while Syrian government helicopters dropped improvised barrel bombs on a village in the country’s south, killing at least nine people, a conflict monitor said.

Many American officials believe that the Russians were never serious about the deal that was sealed in Geneva. The officials argue that the Russians were looking for an excuse that would derail it and keep a status quo in which they have more control over events in Syria than any other power, with the possible exception of Iran. If so, the accidental bombing made that process easier.

Mr. Kerry faced many skeptics in Washington that the arrangement he worked out with his Russian counterpart, Sergey V. Lavrov, would ever work. Chief among them was Defense Secretary Ashton B. Carter, the only senior member of the administration to vocally oppose the deal on the night Mr. Kerry reached it in Geneva. Mr. Carter feared that the accord would reveal too much to the Russians about American targeting intelligence, and argued that Moscow was cynically dragging out the process in President Obama’s final months in office.

Mr. Kerry had argued that it was worth testing the Russians on their willingness to act. But on Sunday, whatever optimism he once had seemed gone.

“The humanitarian assistance is supposed to be flowing,” Mr. Kerry said. “The regime once again is blocking it. So Russia’s client, Russia’s supported friend, is the single biggest blockade to the ability to move forward here.”

But the deadly bombing underscored how difficult it has been to ensure that the American and Russian militaries do not become entangled on Syria’s complicated battlefield, much less to coordinate their targeting.