But a cease-fire is essential, primarily to help the refugees and the civilians still in Idlib, but also to prevent an escalation between Turkey and Russia and to facilitate the start of negotiations to put a formal end to the war. Russia and Turkey have cut deals before in Syria, and they are talking now, though without any results so far. Nudging them toward an agreement is where American, European and United Nations efforts should be focused.

Mr. Erdogan’s main immediate interest in the Idlib fight is to prevent the mass of refugees from crossing into Turkey. But he is also apparently trying to gain some leverage for postwar negotiations to ensure that the Kurds in northeastern Syria are kept away from Turkey. Working all angles, Mr. Erdogan has tried to cultivate a close relationship with Vladimir Putin, including a purchase of Russian missile defense systems that angered the United States, while threatening military action against Russian-backed Syrian forces.

On Saturday, Mr. Erdogan called Mr. Trump to seek support, and his government suggested it might receive some Patriot missiles from the United States to deter Russia. It was after this disclosure that Russian airstrikes killed two Turkish soldiers and wounded five in Idlib, as if to underscore the risk of escalation. But it is dubious that a show of American support would make a difference; the dispute between Mr. Erdogan and Mr. Putin is over terms of their disengagement.

Mr. Putin, however, has made clear that his priority is to end the Syrian war. The Syrian forces have already achieved their main objective in the Idlib area, regaining control over major highways, and the Russians are said to have proposed leaving a nine-mile-wide Turkish-controlled strip inside Syria along the Syrian-Turkish border for refugee camps, which would presumably be accessible to international aid organizations. Mr. Erdogan has demanded a broader area, but the Russians see no reason to negotiate.

At this stage of this tragic war there is no good outcome, given the near certainty of Mr. Assad’s victory, and however he may maneuver and fulminate, Mr. Erdogan does not have a strong hand. His options are to try a counteroffensive, where Russia’s air power would be decisive; or do nothing, which would potentially drive a million more refugees into Turkey; or try to cut as good a deal as he can get. Given the horror of this war, just putting an end to the shooting and preventing another humanitarian disaster would be progress.