After a meeting at the World Economic Forum in Davos with the Ukrainian leader on Thursday that lasted about an hour, Trump said they had a "good" discussion but provided no further details on the substance of the conversation.
On Wednesday, Trump had said a deal to end the conflict was "reasonably close".
"I think the meeting with President Zelenskiy was good. It's an ongoing process," Trump told reporters, saying that US envoys were heading for talks in Moscow on Thursday.
Asked what his message was for Putin, Trump replied: "The war has to end."
Zelenskiy had said earlier this week he would only travel to Davos if he could sign agreements with Trump on US security guarantees and post-war reconstruction funding for Ukraine but there was no indication after the meeting that a breakthrough had been made.
The two leaders have met about half a dozen times face-to-face since Trump returned to the White House last year and upended US policy on Ukraine by embracing diplomacy with Russia.
Zelenskiy, saddled with an energy crisis at home from Russian air strikes that have left swathes of the capital and other regions without power and heating, was due to deliver a speech after his meeting with Trump, his spokesperson said.
"If both sides want to solve this, we're going to get it solved," US envoy for Ukraine Steve Witkoff told an audience at the World Economic Forum on Thursday morning.
"I think we've made a lot of progress."
Witkoff has held talks in recent days with Ukrainian officials in Davos, following weekend discussions in Florida.
He was due in Moscow with fellow US envoy Jared Kushner - Trump's son-in-law - later on Thursday for talks with Putin.
The Kremlin said Putin's meeting with Witkoff and Kushner will take place after 7 to 8pm Moscow time.
After those discussions, negotiators would head directly to Abu Dhabi, Witkoff said on Thursday, "where there will be military-to-military talks and discussion of the prosperity package".
