President Trump on Monday backed off his demand that Russia declare an immediate cease-fire in Ukraine, instead endorsing President Vladimir V. Putin’s call for negotiations between Ukraine and Russia.

After a two-hour phone call with Mr. Putin, Mr. Trump said the Russian leader had agreed to “immediately” start direct negotiations with Ukraine toward a cease-fire and a broader peace deal to end the war. He said the conditions would be negotiated directly between the warring countries “because they know details of a negotiation that nobody else would be aware of.”

It was a shift from Mr. Trump’s recent threats of more pressure on Russia, such as when he raised the prospect of new banking sanctions in April because Mr. Putin may not “want to stop the war” and “has to be dealt with differently.”

Mr. Trump also appeared enthusiastic to surrender his mediating role to a higher power: the pope. In his statement, Mr. Trump said the Vatican had expressed interest in hosting the upcoming negotiations, and urged: “Let the process begin!”

But while Mr. Trump presented the start of peace talks as a concession by Mr. Putin, he was largely endorsing Mr. Putin’s own approach, given that Russia has responded to calls to stop the fighting by proposing extended negotiations.

Now, Mr. Trump appears to be prepared to step back and urge Russia and Ukraine to make a deal directly with each other. President Volodymyr Zelensky of Ukraine expressed concern about that, saying on Monday after he held two calls with Mr. Trump that “the negotiation process must involve both American and European representatives at the appropriate level.”