Trump said talks to end the war were "getting much closer than people realise".
"And President Putin wants it to end. I will tell you that very strongly. Good call, and President Zelenskiy actually wants it to end now," he said in reference to Ukrainian President Volodymyr Zelenskiy during an event at the White House.
"I had a very good call, and I think ... we're getting close to getting it done," Trump said.
Speaking ahead of a NATO summit starting in Ankara on Tuesday, Trump said: "And we're going to be going to NATO and we're going to be talking about it and we, I think, we're going to get it. I think we're going to get it ended."
The Kremlin said on Monday that Putin and Trump had agreed in a weekend call that they would talk again "in the near future," suggesting they are likely to talk this week during or after the NATO summit.
Trump is planning to meet Zelenskiy on Wednesday at the NATO summit, a senior US official said on Sunday.
The idea, the official said, was to make a renewed push to end the war in Ukraine.
The same official said Trump would likely follow up with Putin after talking to Zelenskiy.
Asked on Monday if Trump would phone Putin after meeting Zelenskiy, Kremlin spokesman Dmitry Peskov told reporters: "Yes, indeed, both President Putin and President Trump have agreed that their contacts will continue in the near future."
Peskov said Trump had held a pretty consistent position on the conflict in Ukraine.
"You know, President Trump, the US president, has a fairly consistent stance, and all these fabrications about him supposedly changing his views like a weather vane are, of course, untrue," Peskov said.
"He is consistent and confident in his understanding of what is happening, but, most importantly, he (Trump) is open to listening to the information that is conveyed to him by Putin."
Ukraine has been warding off a full-scale Russian invasion since February 2022.
Recent large-scale Russian missile attacks have claimed multiple lives in Kyiv and other Ukrainian cities while Ukraine has targeted Russia's oil sector and attacked links between Russia and the Crimean peninsula.
with DPA
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