Ukrainian President Volodymyr Zelenskyy made his 15 minutes with US President Donald Trump in the Vatican—and before Pope Francis' funeral—count, urging Trump to take a tougher line with Russian President Vladimir Putin, and reprioritize a ceasefire, two sources briefed on Saturday's meeting tell Axios, the latter reports.

Accordingly, Zelenskyy's advisers were divided about whether he should even risk the tête-à-tête after the disaster in the Oval Office. But after it, Zelenskyy felt he'd managed to shift Trump's thinking about Putin for the first time, the sources say.

And on his way back to the U.S., Trump made a rare threat to Putin in response to a massive aerial attack on Kyiv.

Zelenskyy's advisers were nervous, and some—still traumatized by the scenes in the Oval on February 28—told Zelenskyy they weren't sure it was a good idea.

Nothing was finalized in advance, and the idea was initially that they would try to meet after the funeral, one of the sources said.

But then the leaders bumped into each other upon arrival. They found a spot to meet alone in St. Peter's Basilica.

Zelenskyy told Trump that Putin would not budge unless Trump applied more pressure, the sources say.

One source said Trump replied that he might have to change his approach to Putin.

Zelenskyy also pushed Trump to return to his initial proposal of an unconditional ceasefire as a starting point for peace talks, which Ukraine accepted but Russia rejected.

One source said Trump seemed to agree.