Pope Leo stressed the need to continue with dialogue aiming at a "just and lasting peace" during a meeting on Tuesday with Ukrainian President Volodymyr Zelenskyy, the Vatican said in a statement.
The pope "reiterated the need for the continuation of dialogue and expressed his urgent desire that the current diplomatic initiatives bring about a just and lasting peace," the statement said.
"In addition, the questions of prisoners of war and the need to assure the return of Ukrainian children to their families were also discussed", said the Vatican, which has mediated between Kyiv and Moscow on the children issue.
Zelenskyy met Leo at the papal residence of Castel Gandolfo, about 30 km south east of the Vatican and is due to see Italian Prime Minister Giorgia Meloni in Rome later in the day.
The talks with the pope and Meloni come amid efforts by Zelenskyy, with the help of European allies, to balance out a US-backed draft peace deal with Russia that is widely seen as favourable to Moscow.
The US and Iran failed to reach an agreement to end their war despite marathon talks that concluded on Sunday in the Pakistani capital Islamabad, jeopardising a fragile ceasefire.
Russia and Ukraine accused each other on Sunday of breaching the 32-hour ceasefire in their four-year war, reporting more than a thousand drone and shelling attacks just hours after the truce began on Saturday to mark Orthodox Easter.
At least 30 people were killed on Saturday in a stampede at the Laferriere Citadel in the northern countryside of Haiti, authorities said, warning that the death toll could rise.
A cyclone battered New Zealand's North Island on Sunday, cutting power to thousands of residents and forcing hundreds to evacuate, as officials warned conditions would worsen through the day.
Negotiations between the United States and Iran appeared to have concluded for now, Iran's government has announced early on Sunday, after a series of talks in Pakistan to end the six-week war between Washington and Tehran.