In an interview with Fox News, Trump said he expected that Putin's course of action would become clear in the next couple of weeks.
Trump also again ruled out US boots on the ground in Ukraine and gave no specifics about the security guarantees he has previously said his country could offer Ukraine under any post-war settlement.
"I don't think it's going to be a problem (reaching a peace deal), to be honest with you. I think Putin is tired of it. I think they're all tired of it but you never know," Trump said.
"We're going to find out about President Putin in the next couple of weeks ... It's possible that he doesn't want to make a deal," said Trump, who has previously threatened more sanctions on Russia and countries that buy its oil if Putin does not make peace.
Ukraine and its European allies have been buoyed by Trump's promise of security guarantees to help end the war during an extraordinary summit on Monday but face many unanswered questions, including how willing Russia will be to play ball.
Ukrainian President Volodymyr Zelenskiy hailed Monday's talks at the White House with the US president as a "major step forward" towards ending the conflict and towards setting up a trilateral meeting with Putin and Trump in the coming weeks.
The path to peace remains deeply uncertain and Zelenskiy may be forced to make painful compromises to end the war, which began with Russia's full-scale invasion in February 2022.
Analysts say more than a million people have been killed or wounded in the conflict.
While the US talks allowed for a temporary sense of relief in Kyiv, there was no let-up in the fighting.
Russia launched 270 drones and 10 missiles in an overnight attack on Ukraine, the Ukrainian air force said, the largest this month.
The energy ministry said Russia had targeted energy facilities in the central Poltava region, home to Ukraine's only oil refinery, causing big fires.
However, Russia also returned the bodies of 1000 dead Ukrainian soldiers on Tuesday, Ukrainian officials said.
Russian negotiator Vladimir Medinsky said Russia received 19 bodies of its own soldiers in return, according to the state-run TASS news agency.
Russia said it had returned 7000 bodies before the latest handover, while claiming Ukraine has transferred fewer than 100 in total.
The Kremlin portrays this as proof that Ukraine has suffered far higher battlefield losses.
Ukraine, meanwhile, noted that among the 1000 bodies returned were five soldiers who had died while being held in Russian captivity.
According to Ukraine's Coordination Headquarters for the Treatment of Prisoners of War, those men should have been released earlier under an Istanbul agreement on exchanging severely wounded soldiers.
Ukraine's allies held talks in the so-called "coalition of the willing" format on Tuesday, discussing additional sanctions to crank up the pressure on Russia.
The grouping has also agreed that planning teams will meet US counterparts in the coming days to advance plans for security guarantees for Ukraine.
NATO military leaders are expected to meet on Wednesday to discuss Ukraine, with US General Dan Caine expected to attend the meeting virtually, officials told Reuters.
Russia has made no explicit commitment to a meeting between Putin and Zelenskiy.
Foreign Minister Sergei Lavrov said on Tuesday that Russia did not reject any formats for discussing the peace process in Ukraine but any meeting of leaders "must be prepared with utmost thoroughness".
Swiss Foreign Minister Ignazio Cassis said on Tuesday his country was prepared to host talks on Ukraine that involve the participation of Putin, despite the arrest warrant issued against him by the International Criminal Court.
French President Emmanuel Macron and Italian Prime Minister Giorgia Meloni have both suggested Geneva as a possible venue for talks involving Putin and Zelenskiy.
with DPA
