US President Donald Trump and Ukrainian leader Volodymyr Zelenskiy, in Rome for the funeral of Pope Francis, met one-on-one in a marble-lined Vatican basilica on Saturday to try to revive faltering efforts to end Russia's war with Ukraine.

Zelenskiy said the meeting could prove historic if it delivers the kind of peace he is hoping for, and a White House spokesman called it "very productive".

The two leaders, leaning in close to each other with no aides around them while seated in St Peter's Basilica, spoke for about 15 minutes, according to Zelenskiy's office, which also released photographs of the meeting.

The meeting at the Vatican, their first since an angry encounter in the Oval Office in Washington in February, comes at a critical time in negotiations aimed at bringing an end to fighting between Ukraine and Russia.

In a post on social media platform Telegram, Zelenskiy wrote: "Good meeting. One-on-one, we managed to discuss a lot. We hope for a result from all the things that were spoken about."

He said those topics included: "The protection of the lives of our people. A complete and unconditional ceasefire. A reliable and lasting peace that will prevent a recurrence of war."

Zelenskiy added: "It was a very symbolic meeting that has the potential to become historic if we achieve joint results. Thank you, President Donald Trump!"

Steven Cheung, White House communications director, said the two leaders had met privately and had "a very productive discussion. More details about the meeting will follow". (Reuters)