Putin's call with Trump lasted just under an hour, according to Russian presidential aide Yuri Ushakov, who briefed reporters afterwards.
Zelenskiy's adviser Dmytro Lytvyn earlier told journalists that the conversation lasted around 30 minutes.
On Ukraine, Ushakov said Trump emphasised the need to end hostilities and stated his readiness to influence European allies and Kyiv toward that goal, including at the upcoming G7 summit.
Trump also said that recent strikes on civilian targets in Russia complicate a settlement — though the White House has not confirmed that, nor commented on the call — and said that ending the war quickly could open the door to "a truly new quality of US-Russian relations," Ushakov quoted him as saying.
Putin, for his part, argued that attacks on Russian civilian infrastructure by Kyiv would not change Ukraine's position on the battlefield, and said that if Zelenskiy wants a meeting with him, "let him come to Moscow," according to Ushakov.
US envoy Steve Witkoff and Trump's son-in-law Jared Kushner are expected to travel to Russia soon, Ushakov said.
The leaders also discussed Iran, where Trump said a US agreement with Tehran was close and that he hoped the results of the talks could be made public today, Ushakov said.
Zelenskiy said in a statement on Telegram Sunday that he had a "wonderful conversation" with Trump.
Beyond congratulating Trump on his birthday, the Ukrainian president said he thanked the US president for supporting Ukraine.
He said they discussed "what could help bring peace closer now," without providing details. Zelenskiy also informed Trump about how Ukraine's position along the eastern front line has improved and strengthened.
"We agreed to discuss more during our meeting at the G7 summit," he said.
The calls came as Trump prepared to mark his birthday with an Ultimate Fighting Championship fight on the White House lawn Sunday evening, an event without precedent in American history.
Once it concludes, Trump is set to fly overnight to France for the G7 summit, where Ukraine is expected to be a major topic of discussion on Tuesday and Zelenskiy is due to join the gathering.
Russia's war in Ukraine has long frustrated Trump, who as a candidate claimed he could end the conflict within 24 hours of taking office.
He has since stopped making such claims and tends to pivot away from the topic when pressed.
He has also grown increasingly vexed by the war between Israel and Iran, which has driven up gas prices, rattled financial markets and stoked concerns about inflation.
The diplomatic exchanges came against the backdrop of continued fighting.
Ukrainian drone attacks killed one person and wounded nine others overnight in a residential building in the regional capital of Russia's Oryol region, Governor Andrei Klychkov said Sunday.
Another drone attack killed one person Sunday in Russia's Bryansk region, local authorities said.
A separate drone strike hit fuel storage facilities in Russia's Yaroslavl region, around 708.1 km from the Ukrainian border, sparking fires.
Zelenskiy said the strike had hit "an oil facility that was important for the reserve of the aggressor state".
Ukraine has stepped up attacks on Russian oil and gas infrastructure in recent months, arguing that the sector funds Moscow's invasion.
with dpa
