“We have not found a magic wand or a silver bullet, but we have relaunched the peace process,” he said. The Paris meeting, he added, was “a very positive step forward.”

The four leaders agreed to meet again in four months.

Mr. Zelensky, under mounting pressure at home from nationalists who accuse him of capitulating to Russia, arrived in Paris with limited room to maneuver and far fewer military or political resources to call on than Mr. Putin. His previous gestures of good will, notably the withdrawal of Ukrainian troops from the front line, have won no reciprocal steps by Russia or the rebels it supports in the regions of Donetsk and Luhansk.

His position was further weakened by the absence of strong support from the United States, something that Ukraine had previously relied on as it struggles to hold its own on the battlefield against Russian troops — which the Kremlin has insisted are not serving soldiers but merely Russians “on vacation” — as well as armed separatists supported by Moscow.

The United States was never been formally involved in shaping or enacting the Minsk agreement, but under President Barack Obama it played a central role in “lassoing the various sides,” said Alina Polyakova, a fellow in the Center on the United States and Europe at the Brookings Institution in Washington.

Mr. Trump has been besieged by impeachment hearings focused on his dealings with Ukraine — specifically, an American delay in delivering promised military aid and the withholding of a much-coveted White House meeting for Mr. Zelensky — and by criticism of repeated foreign policy shifts that favor Mr. Putin.

Perhaps as a result, the American president has shown little inclination to get involved in the nitty-gritty details of settling the war, telling Mr. Zelensky when they met in New York in September: “I really hope you and President Putin get together and can solve your problem.”

Many Trump administration officials who advocated supporting Ukraine in its struggle against Russia have resigned or been sidelined. The State Department’s special envoy for Ukraine and its point man for settling the conflict in the east, Kurt D. Volker, resigned in September.