Trump made the comment to reporters a day after he showed frustration with Russia and told it to "get moving" on reaching a deal.
"I think Ukraine-Russia might be going okay, and you're going to be finding out pretty soon," Trump told reporters on Air Force One on Saturday.
"There's a point at which you just have to either put up or shut up and we'll see what happens, but I think it's going fine."
On Friday, Trump's special envoy Steve Witkoff held talks with Russian President Vladimir Putin about the search for a peace deal.
The talks came at a time when US-Russia dialogue aimed at agreeing a ceasefire ahead of a possible peace deal to end the war appeared to have stalled over disagreements around conditions for a full pause in hostilities.
Trump has shown signs of losing patience and has spoken of imposing secondary sanctions on countries that buy Russian oil if he feels Moscow is dragging its feet on a deal.
Earlier on Saturday, Russian Foreign Minister Sergei Lavrov praised Trump for what he said was a better understanding of the Ukraine conflict than any other Western leader.
"When we speak about eliminating root causes of any conflict, including the Ukrainian conflict, this is the only way to resolve the problem and to establish long-lasting peace. Remove root causes," Lavrov said at the Antalya Diplomacy Forum in southern Turkey.
"President Trump was the first and so far, I think, almost the only one among the Western leaders who repeatedly, with conviction, several times stated that it was a huge mistake to pull Ukraine into NATO. And this is one of the root causes which we quoted so many times."
Putin, who launched Russia's invasion of Ukraine in February 2022, has long cast Ukraine's tilt to the West, including its desire to join NATO, as a threat to Russia.
Commenting on an agreement between Ukraine and Russia to pause strikes on each other's energy facilities, Lavrov said that Moscow has been keeping its word and accused Kyiv of striking Russian energy infrastructure almost every day.
"I gave to our colleagues from Turkey, to (Foreign) Minister (Hakan) Fidan, what we gave to the Americans, to the UN, to the OSCE - the list of facts listing the attacks by Ukraine during the last three weeks against Russian energy infrastructure."
Ukraine has made similar accusations against Russia since the US-backed moratorium was approved.Â
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