A Kremlin spokesperson said Mr Putin and Mr Trump had agreed to meet, with the Russian president inviting the US leader to visit Moscow.
Mr Trump added that his phone conversation with Mr Zelenskyy "went very well", suggesting that "he [Mr Zelenskyy], like President Putin, wants to make PEACE".
Meanwhile at a White House news conference on Wednesday, press secretary Karoline Leavitt said she was "not aware of" Mr Trump putting any preconditions on his meeting with Mr Putin.
"President Putin, for his part, mentioned the need to eliminate the root causes of the conflict and agreed with Trump that a long-term settlement can be achieved through peaceful negotiations," said Kremlin spokesperson Dmitry Peskov.
Meanwhile, Ukraine's president wrote on X that he had a "meaningful conversation" by phone with Mr Trump to discuss "opportunities to achieve peace" and the preparation of a document governing security and economic cooperation.
