Russian President Vladimir Putin told his US counterpart Donald Trump Saturday that Moscow was ready to hold a fresh round of peace talks with Kyiv after 22 June, once the sides complete exchanging prisoners and soldiers' bodies.

Ukraine's leader Volodymyr Zelensky meanwhile did not mention whether Ukraine would agree to the next round of talks, only saying that "the exchanges will be completed and the parties will discuss the next step."

Putin and Trump held a call for the fifth time since the Republican took office and sought to reset relations with Moscow, in a stark pivot from the approach of his predecessor Joe Biden's administration.

Trump's approach has stunned Washington's allies, raising doubts about the future of US aid to Kyiv and leaving Europe scrambling to work out how it can fill any gap in supplies if Trump decides to pull US military, financial and intelligence support.

"Both leaders expressed satisfaction with their personal relations," during the call, in which they also discussed the escalating conflict between Iran and Israel, the Kremlin said.

It added that the presidents "communicate in a businesslike manner and seek solutions to pressing issues on the bilateral and international agenda, no matter how complex these issues may be."

Zelensky urged the United States to "shift tone" in its dialogue with Russia, saying it was "too warm" and would not help to end the fighting.

"Any signals of reduced aid, or of treating Ukraine and Russia as equals, are deeply unfair. Russia is the aggressor. They started this war. They do not want to end it," the Ukrainian President said on X.

The Ukrainian leader also warned against a drop in aid due to the escalating Israel-Iran conflict, at a time when European support is stalling without US engagement.

The recent escalation sparked anxiety in Kyiv about future supplies of military aid, fearing Washington might relocate more resources to beef up the defense of its close ally Israel which unleashed a large-scale attack on Iran Friday.

"We would like to see aid to Ukraine not decrease because of this," he said. "Last time, this was a factor that slowed down aid to Ukraine."

More soldiers exchanged

Earlier on Saturday, Ukraine and Russia swapped prisoners in the fourth such exchange this week, part of a large-scale plan to bring back 1,000 wounded prisoners from each side and return bodies of killed soldiers.

The prisoner agreement was the only visible result of two recent rounds of talks in Istanbul.

Photos published by Zelensky on Telegram showed men of various ages, mostly with shaved heads, wearing camouflage and draped in Ukrainian flags.

Some were injured, others disembarked from buses and hugged those welcoming them, or were seen calling someone by phone, sometimes covering their faces or smiling.

Moscow's defense ministry released its own video showing men in uniforms holding Russian flags, clapping and chanting "Glory to Russia" and "hooray", some raising their fists in the air. 

As part of the Istanbul agreements, Kyiv also said it had received another 1,200 unidentified bodies from Russia. 

It said Moscow had said they were those of "Ukrainian citizens, including military personnel." Ukraine did not say whether it returned any bodies to Russia.

Russia has rejected calls to halt its three-year offensive. It has demanded Ukraine cede territory and renounce Western military support if it wants peace.

Since Russia sent troops into Ukraine in February 2022, the assault has forced millions of people to flee their homes as towns and cities across eastern Ukraine have been flattened by heavy bombardments.

Meanwhile, Russia intensified its advances along the front line, especially on the northeastern Ukrainian region of Sumy, where it seeks to establish a "buffer zone."

By doing it, Moscow seeks to protect its bordering region of Kursk, previously partly occupied by Ukraine. 

Zelensky said Russia's advance on Sumy was stopped and that Kyiv's forces had managed to retake one village.

He also denied Moscow's earlier claims that its troops entered the Dnipropetrovsk region. 

He said 53,000 Russian soldiers were involved in the Sumy operation.