Francis is buried in a place of solace for him.

It came at a critical moment. The United States has presented Ukraine with a plan for a cease-fire in its war with Russia, leading to a postwar plan that would give Russia de facto control over all of the lands it has illegally seized since the invasion began three years ago. The proposal also includes a major reversal of American policy: a formal recognition by the United States that Crimea, seized by Moscow in 2014, is now Russian territory.

Mr. Zelensky said this past week that Ukraine would never make that concession, noting that it would violate Ukraine’s Constitution; most of the other nations in Europe would almost agree with Mr. Zelensky’s view. But the Ukrainian leader has a counterproposal of his own, Ukrainian officials said, one that would end the conflict on far less generous terms for Russia, and would include billions of dollars in reparations for Ukraine, paid by Russia.

The White House did not respond to queries about the specifics of the meeting in Vatican City. But it was a remarkable scene: an impromptu meeting between two men who have made no secret of their deep dislike and distrust for each other. In the minutes after they last saw each other, Mr. Zelensky was essentially evicted from the White House, a lunch for the two men left uneaten and an economic accord allowing the United States to help exploit much of Ukraine’s minerals left unsigned.

The meeting at the Vatican came just as Mr. Trump was trying to push Mr. Zelensky and President Vladimir V. Putin of Russia into direct talks. “They are very close to a deal,” Mr. Trump wrote on Truth Social late Friday, after landing in Rome. “The two sides should now meet, at very high levels, to ‘finish it off.’”

His enthusiasm may be premature. The proposal turned out by the Trump administration and Mr. Zelensky’s alternative showed a huge gap even on the question of what the Russians should be offered. And neither of the proposals meet several of Mr. Putin’s demands, including that the size of Ukraine’s military be sharply limited.

Mr. Zelensky posted a positive-sounding description of the meeting on X that made clear that he had learned one lesson from his Oval Office encounter: Always show gratitude, even if he and Mr. Trump differ significantly on the terms for ending the war.

“Good meeting,” he wrote, saying that among the points covered were “full and unconditional ceasefire,” and a “reliable and lasting peace that will prevent another war from breaking out.” The last was particularly important: Mr. Trump’s proposal has only vague security guarantees for Ukraine. The Ukrainian proposal is far more specific, calling for a European peacekeeping force with the U.S. providing backup.

“Very symbolic meeting that has potential to become historic, if we achieve joint results,” he wrote, careful to use the word “potential.” He ended with: “Thank you @POTUS.”

Since his inauguration, Mr. Trump has made clear that he wanted his first trip overseas in this term to be to the Middle East, starting with Saudi Arabia, the site of his initial visit during his first term in office. But on Saturday morning, he was in Europe, making his way to Vatican City to pay his respects at the pontiff’s funeral.

As the ceremonies began, Mr. Trump was surrounded by European leaders he has been denouncing as freeloaders unwilling to pay their share of the continent’s defense, and leaders of the European Union, which he said was “formed in order to screw the United States.”

On his way to Italy on Friday, Mr. Trump told reporters on Air Force One that he was attending the funeral “out of respect” for Francis, noting, “I won the Catholic vote.”

The seating plan released by the Vatican had guests seated in their group in alphabetical order based on their country’s name in French. That put Mr. Trump in the front row between the leaders of Finland and Estonia, — two countries deeply worried about Russia’s “shadow war” against their countries — and just down from President Emmanuel Macron of France. Mr. Trump, Mr. Macron and Mr. Zelensky all chatted briefly before the services began.

Mr. Trump’s every handshake and conversation at the funeral was watched for meaning. He briefly greeted Ursula von der Leyen, the president of the European Commission, the executive arm of the European Union, who was sitting a few chairs down from Mr. Trump. White House reporters traveling with the president, but kept at a considerable distance, reported that the two appeared to chat, funereal protocols aside. In the past three months, Ms. von der Leyen was conspicuously absent from the leaders visiting the White House.