“The eyewitnesses will tell you what happened,” Mr. Kerry said, in a direct confrontation with Russia of a kind rarely seen at the Security Council since the Cold War. “The place turned into hell and fighter jets were in the sky.”

With his new proposal, Mr. Kerry was also making what amounts to an 11th-hour effort to test Russian intentions in Syria, where the Kremlin has increasingly engaged militarily to defend Mr. Assad. Mr. Lavrov’s spokeswoman, Maria Zakharova, who was accompanying him, suggested after Mr. Kerry spoke that the Russians were not enthused by his ideas.

“It’s about nothing,” she said. “That was a show.”

In private, senior Obama administration officials acknowledge that the very viability of the agreement with the Russians is in question. Yet none of the players wanted to walk away and concede that the effort had failed.

Mr. Kerry said the flight ban should be in “key areas.” American officials declined to specify them. But they said he was referring to parts of northwest Syria that are in dire need of aid, including cities like Aleppo, where the opposition is prevalent.

The flight ban proposal will be discussed Thursday at a meeting in New York of the International Syrian Support Group, a multinational body that is led by Mr. Kerry and Mr. Lavrov. A more definitive Russian response to the proposal may come then.

One of the crucial American tasks in those cities is to separate Syrian opposition groups that the United States has supported and groups like the Nusra Front, a Qaeda affiliate that now calls itself the Levant Conquest Front. But fulfilling that task has proved far more difficult in Aleppo, for example, than it seemed in the negotiating room in Geneva.

While separating the American-backed groups from their tactical alliances with the Nusra Front sounds logical, for the rebels it would often mean abandoning their home territory, leaving Nusra unchallenged and opening their towns to an American-Russian bombing campaign. Others groups would have to fight Nusra, something they do not have the capability to do.