At a press conference in Moscow after Saturday's scaled-back Victory Day parade marking the end of World War II, Putin said: "Anyone who wants to meet me has to come to Moscow."
Putin said this wasn't a direct invitation to Zelenskiy but that he was prepared to meet him.
"We can also meet somewhere other than Moscow but only if a long-term peace agreement has been reached beforehand," Putin said.
"I think that the matter is coming to an end," Putin told reporters of the Ukraine war.
Zelenskiy has ruled out a trip to Moscow.
Putin dismissed reports about a message from Zelenskiy that Slovakian Prime Minister Robert Fico said he wanted to deliver.
"There was no personal message."
Fico had reported Zelenskiy's willingness to hold talks, he said.
"But this is not the first time we have heard that."
Putin said he could imagine his friend and former German chancellor Gerhard Schröder as a mediator.
Although the US had so far sought to mediate in the conflict, he said he could see Schroeder acting as a mediator from the European side.
"Of all European politicians, I would prefer talks with Schröder."
Schröder and Putin are considered close friends.
The Russian president accused Europe of wanting to escalate the conflict in Ukraine.
However, he said Europe knew "that this game could become expensive".
Victory in Ukraine, though, has been elusive for Russia.
During four years of the deadliest European conflict since World War II, Russian forces have so far been unable to take the whole of the Donbas region of eastern Ukraine where Ukrainian forces have been pushed back to a line of fortress cities.
The war has killed hundreds of thousands of people, left swathes of Ukraine in ruins and drained Russia's economy while Russia's relations with European countries are worse than at any time since the depths of the Cold War.
The Financial Times reported on Thursday that European Union leaders were preparing for potential talks.
The Kremlin said last week that it was for European governments to make the first move, as they were the ones who severed contact with Russia in 2022 after the start of the war in Ukraine.
Ukrainian army spokesman Viktor Trehubov said earlier on Saturday that Russian and Ukrainian forces were making use of the three-day ceasefire to rotate troops and bring in reinforcements.
"The Russians are in fact taking a break today and are using it to bring up reinforcements, to rotate forces and to restore their offensive capabilities," he said.
with Reuters
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