Trump, who has been pressing Russia to agree a 30-day unconditional ceasefire, said he would speak with Putin by phone on Monday. Kremlin spokesman Dmitri Peskov told the state TASS news agency the call was “being prepared”.
That came a day after direct talks between the two countries led to an agreement for another exchange of prisoners.
Zelensky, denouncing the attack and Russia's refusal so far to agree a ceasefire, repeated his call for fresh sanctions against Moscow.
On Sunday morning, local authorities in the Kyiv region reported that a woman had been killed in a drone attack in Obukhiv district.
On Friday in Istanbul, the first direct Ukraine-Russia talks since the spring of 2022 -- shortly after Moscow's full-scale invasion that February -- led to an agreement to exchange 1,000 prisoners each.
Trump denounces 'bloodbath'
“We consider it possible, but only as a result of the work and upon achieving certain results in the form of an agreement between the two sides,“ the Kremlin’s spokesperson said.
The Kremlin said that first the POW swap had to be completed and both sides need to present their visions for a ceasefire before fixing the next round of talks.
The head of Ukraine's military intelligence, Kirillo Budanov, told broadcaster TSN he hoped the exchange would happen next week.
Afterwards, he added, he would speak to Zelensky and NATO officials, expressing hope that a “ceasefire will take place, and this very violent war... will end”.
Trump has argued that “nothing’s going to happen” on the conflict until he meets Putin face-to-face.
US Secretary of State Marco Rubio welcomed the latest prisoner exchange in a telephone call with Russian Foreign Minister Sergei Lavrov.
If Russia and Moscow can both provide “serious and viable” proposals “then there’s been real progress, and we can work off of that,“ Rubio said.
Elsewhere on the frontlines, the Russian army said its troops captured Oleksandropil village in the eastern Donetsk region, site of some of the most intense fighting.
“Yesterday in Istanbul, everyone saw a weak and unprepared Russian delegation with no significant powers. This must change. We need real steps to end the war,“ Zelensky said Saturday.
Macron said European nations were coordinating with Washington on additional sanctions should Moscow continue to refuse an “unconditional ceasefire.”
During the Istanbul talks, the Ukrainian side said Russia had made “unacceptable” territorial demands.
Moscow claims annexation of five Ukrainian regions -- four since its 2022 invasion, and Crimea, which it annexed in 2014.
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