Meanwhile, Ukrainian President Volodymyr Zelensky did not say whether Ukraine had agreed to the next round of talks. He only said that"the exchange will be completed and the parties will discuss the next step."
Putin and Trump spoke for the fifth time since the Republican took office as US president in January. It was their third phone conversation in the past month.
"Both leaders expressed satisfaction with their personal relations during the phone call," the Kremlin said.
The Moscow statement 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."
As Putin's adviser Yuri Ushakov told the Russian propaganda agency TASS, Putin has condemned Israeli attacks on Iranian nuclear and military facilities and offered to mediate in resolving the conflict.
Ushakov informed that Putin had congratulated Trump on his 79th birthday.
Zelensky earlier on Saturday urged the US to"change the tone" in its dialogue with Russia, saying it was"too lukewarm" and would not help end the war.
"Any signals about reducing aid or treating Ukraine and Russia as equal countries are deeply unfair. Russia is the aggressor. It started this war. It does not want to end it," the Ukrainian president wrote on the "X" platform.
The Ukrainian leader also warned against reducing aid to Ukraine due to the escalation of the Israeli-Iranian conflict at a time when European support without US involvement is difficult.
Ukraine and Russia on Saturday carried out their fourth prisoner exchange this week, part of a broader plan for each side to recover 1,000 wounded prisoners and the bodies of fallen soldiers.

%3Aformat(webp)%2Fnginx%2Fo%2F2025%2F06%2F04%2F16895540t1h280c.jpg&w=3840&q=75)