The phone call on Tuesday, which the Kremlin said lasted an hour, followed a weekend visit to Moscow and Kyiv by US envoys Steve Witkoff and Jared Kushner, who are trying to revive stalled talks designed to find a way to end the fighting.
Russia had resumed drone and missile attacks on Kyiv after their departure.
The overnight attack caused fires in several districts across the Ukrainian capital, damaging at least 14 high-rise buildings, a dorm, a school, a clinic, warehouses and other sites, officials said.
"Kyiv was exploding and burning," Katarina Mathernova, the EU ambassador to Ukraine, said in a social media post.
Explosions reverberated across the city as Russia kept menacing it with jet-powered drones into Tuesday afternoon.
Two people were killed in a strike on a warehouse, bringing the total death toll in the city to five, Klitschko said. Close to 30 people have been injured, authorities said.
The weekend diplomacy did not appear to result in any immediate public breakthrough although they did raise the possibility that three-way talks between Russia, Ukraine and the United States could be resumed. The Kremlin, which has said it does not rule that out, made no mention of the possibility in its readout of the Putin-Trump call.
Instead, Kremlin aide Yuri Ushakov told reporters that the two leaders had rated the US envoys' weekend diplomacy "with a plus sign" and that Putin had told Trump what he believed the United States could do to help end the conflict and given him an assessment of what the situation on the battlefield was.
Trump, Ushakov said, had made it clear he wanted the war quickly finished.
"Donald Trump clearly emphasised the desirability of bringing the conflict to an end as soon as possible, which would immediately open up prospects – impressive and far-reaching ones at that – for the full restoration of relations between the US and Russia," said Ushakov.
"In his view, this would have a particular impact on trade and economic ties, promising enormous benefits for both countries. Donald Trump is keen to see a breakthrough achieved during his presidency. Vladimir Vladimirovich Putin supported this approach."
Russia and Ukraine remain far apart on how to end the war, the deadliest in Europe since World War Two, and both sides have escalated their attacks on each other in recent months. A person close to the Kremlin, speaking before the trip by Trump's envoys, said Putin remained intent on taking full control of the remainder of the Donetsk region in eastern Ukraine, something Kyiv has vowed to continue fiercely opposing with every weapon at its disposal.
Ushakov - who said Putin and Trump had also agreed on the need to continue prisoner exchanges - said he was not able to get into more detail about what had been discussed, but described the conversation as constructive and said the two leaders had agreed they would stay in touch and speak to each other by phone again if the need arose.
He said Putin had told Trump that Russia had no hostile intentions when it came to Europe despite repeated claims to the contrary by various European politicians.
"In light of speculation regarding Russia's alleged hostile intentions towards European states, it was emphasised that we have absolutely no aggressive plans whatsoever towards Europe," said Ushakov.
"The myths being spread about the Russian threat merely serve as a pretext for Europeans to ramp up their support for Ukraine and their own military spending," he added.
