The Ukrainian leader has repeatedly called for Putin to meet him, saying it is the only way to negotiate an end to Russia's war in Ukraine.
US President Donald Trump, who has vowed to end what he calls the "bloodbath" in Ukraine, said he had begun the arrangements for a Putin-Zelenskiy meeting after a call with the Russian leader on Monday.
Zelenskiy accused Russia of stalling.
"The Russians are doing everything they can to prevent the meeting from taking place," he said on Friday at a press conference in Kyiv with NATO Secretary General Mark Rutte.
Russian Foreign Minister Sergei Lavrov told NBC in an interview on Friday that there is no agenda for such a summit.
"Putin is ready to meet with Zelenskiy when the agenda would be ready for a summit. And this agenda is not ready at all," he said.
The statement echoed Moscow's established rhetoric about a leaders' meeting being impossible unless certain conditions were met.
Asked for his response to Lavrov's comments and what the next steps are, Trump told reporters: "Well, we'll see. We're going to see if Putin and Zelenskiy will be working together. It's like oil and vinegar a little bit".
Thousands of Ukrainian civilians have been killed in the full-scale invasion of Ukraine that Russia launched in 2022.Â
Analysts estimate that more than a million soldiers on both sides have been killed or wounded and fighting is continuing unabated.
Russia has maintained its longstanding demand for Ukraine to give up land it still holds in two eastern regions.
It also proposes to freeze the front line in two more southerly regions Moscow claims fully as its own and possibly hand back small pieces of other Ukrainian territory it controls.
Zelenskiy, meanwhile, has dropped his demand for a lengthy ceasefire as a prerequisite for the leaders' meeting, even though he has previously said Ukraine cannot negotiate under the barrel of a gun.
On Friday, he called on his country's allies to pressure Russia into "at least a minimally productive position," including by applying fresh sanctions if Russia showed no interest in moving towards peace.
Speaking at a joint press conference with Rutte, Zelenskiy said they had discussed security guarantees for Ukraine by other states.
He said the guarantees ought to be similar to NATO's Article 5, which considers an attack on one member of the alliance as an attack against all.
"This is the beginning of a big undertaking, and it is not easy, because guarantees consist of what our partners can give Ukraine, as well as what the Ukrainian army should be like, and where we can find opportunities for the army to maintain its strength," Zelenskiy said.
Rutte said NATO allies and Ukraine are working together to make sure security guarantees are at such a robust level that Russia will never try to attack again.
"Robust security guarantees will be essential, and this is what we are now working on to define", he said.
On Thursday, military chiefs from the US and a number of European countries presented options to their national security advisers for providing security guarantees to Ukraine, officials said.
Zelenskiy's chief of staff Andriy Yermak, told Ukrainian television on Friday that Kyiv expects to see the first drafts of the security guarantees proposals next week.
