He spoke after the Kremlin reported the two leaders discussed a temporary Ukraine ceasefire to mark the anniversary of the end of World War II next month.
"We had a good talk, I've known him a long time," Trump said.
The two leaders had their last publicly reported phone call on March 9.
Trump, speaking to reporters as he met with astronauts from the Artemis II mission in the Oval Office, said he suggested "a little bit of a ceasefire" in the war in Ukraine in his phone call with the Russian leader.
"And I think he might do that," Trump said, then asked reporters whether Putin had already announced a ceasefire.
Putin announced a similar truce last year that lasted three days but was not agreed with Ukraine.
Trump said Putin offered to help on the issue of Iran's enriched uranium, a key obstacle to a deal to end the Iran war, but "I said I'd much rather have you be involved with ending the war with Ukraine".
"I said, before you help me, I want to end your war," Trump said.
Kremlin aide Yuri Ushakov did not say what proposals Putin had made on Iran.
Russia has previously offered to take enriched uranium out of the country.
Ushakov told reporters Putin had proposed the temporary ceasefire in Ukraine for celebrations on May 9 to mark the Soviet Union's part in the defeat of Nazi Germany in World War II.
He said Trump reacted positively.
Ushakov added that Trump, in a friendly and businesslike conversation lasting more than one and a half hours, had said he believed a deal to end the Ukraine war was close.
The talks came as three women were killed in a Ukrainian attack on Russia's border region of Belgorod, the regional governor said.
Eight more people were injured, Vyacheslav Gladkov wrote on Telegram.
A bus was hit in the village of Voznesenovka in the Shebekinsky district near the border with Ukraine, he said.
Ukraine also struck what it said was an oil pumping station 1500km inside Russia near the Ural Mountains with drones overnight, and President Volodymyr Zelenskiy said his country's forces will keep increasing the range of their strikes.
Zelenskiy said Ukraine's security service had reported a successful strike deep inside Russia, calling it "a new stage in the use of Ukrainian weapons to limit the potential of Russia's war" in a post on X.
He posted a video of smoke billowing into the sky from what he described as a Ukrainian strike inside Russia.
Zelenskiy did not identify the target but Ukraine's SBU security service later said Ukrainian drones had hit a Russian oil pumping station near the city of Perm overnight.
The Russian governor there reported a fire at an industrial facility.
"The straight-line distance is over 1500km. We will continue to extend these ranges," Zelenskiy added.
with DPA
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