The meeting lasted for half an hour, according to Ukraine, and is the first conversation between them since the notable quarrel at the White House in late February.
Zelensky and Vance discussed "the situation at the front, preparations for the conversation (between Trump and Putin) on Monday, the possibility of sanctions against Russia if there are no results, and a ceasefire", according to a Ukrainian source.
The two politicians met in connection with the new pope's installation ceremony in the Vatican and shook hands then.
Vance will also meet EU chief Ursula von der Leyen and Italian Prime Minister Giorgia Meloni on Sunday, a meeting expected to deal with trade tariffs between the US and EU.
