The two presidents spoke at a joint news conference after meeting at Trump's Mar-a-Lago estate in Palm Beach.
Trump said it would become clear "in a few weeks" whether negotiations to end the war would succeed.
Zelensky said Kyiv and Washington had all but reached agreement on security guarantees for Ukraine.
Trump said the two sides were about 95 percent of the way to such an agreement, and that he expected European countries to take on a major role, with US support.
Territorial issues, including the future of Ukraine's eastern Donbas region sought by Russia, remain unresolved, the Reuters news agency reported.
"It’s unresolved, but it’s getting a lot closer," Trump said. "That’s a very tough issue."
Trump said he spoke with Russian President Vladimir Putin shortly before Zelensky arrived in Florida, describing the call as "productive," and said he planned to speak with Putin again after meeting the Ukrainian leader.
Trump said he and Zelensky also held a phone call with several European leaders, including Polish President Karol Nawrocki, during the meeting.
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Source: CNN, Reuters, IAR, PAP, TVN24
Click on the audio player above to hear a report by Marcin Matuszewski.