Zelenskiy told the media in a WhatsApp chat that Kyiv was committed to continuing talks on how to end the war triggered by Russia's 2022 full-scale invasion and he was ready to meet Putin in any format.
US President Donald Trump said on Sunday he and Zelenskiy were "maybe very close" to an agreement to end the war although "thorny" territorial issues lingered.
He was more cautious than Zelenskiy on security guarantees, but said they were 95 per cent of the way to such an agreement and that he expected European countries to "take over a big part" of that effort with US backing.
On Tuesday, Russia said its negotiating stance would toughen after it accused Kyiv of attacking one of Putin's Russian presidential residences - an allegation that Kyiv said was baseless and intended to scuttle arduous peace talks.
Zelenskiy said in his WhatsApp chat that a US troop presence in Ukraine would be a major security boost for Kyiv.
"Of course, we are discussing this with President Trump and with representatives of the (Western) coalition (supporting Kyiv). We want this. We would like this. This would be a strong position of the security guarantees," he said.
The White House had no comment on the issue of dispatching US troops to Ukraine under any peace settlement with Russia.
Zelenskiy said he was willing to meet Putin despite the deep lack of mutual trust he underlined on Monday.
"I told President Trump, European leaders I am ready for any format of meeting with Putin. I am not afraid of any format ... The main thing is for Russians not to be afraid," he said.
Russia said on Monday Kyiv had targeted a presidential residence in the Novgorod region with 91 long-range attack drones, all of which it said it had intercepted.
Russian Foreign Minister Sergei Lavrov described the alleged attack as "state terrorism" and said Moscow had already identified targets for retaliatory strikes in Ukraine.
The Kremlin provided no physical evidence of the alleged incident, saying it would retaliate and review its negotiating stance but would not quit talks on a possible peace deal.
Zelenskiy said earlier on Tuesday: "This alleged 'residence strike' story is a complete fabrication intended to justify additional attacks against Ukraine, including Kyiv, as well as Russia's own refusal to take necessary steps to end the war. Typical Russian lies."
In Paris, a source close to French President Emmanuel Macron said there was no substance to corroborate Moscow's accusation of an attack on Putin's residence.
"Ukraine and its partners are committed to a path of peace, while Russia has chosen to continue and intensify its war against Ukraine. This is in itself an act of defiance against President Trump's peace agenda," the source said.
The White House declined further comment on the reported attack on Putin's residence after Zelenskiy said he brought it up with Trump, who on Monday said he was informed of the matter by Putin and was angry about it. Asked if there was evidence of such an attack, Trump said, "We'll find out."
In Warsaw, Polish Prime Minister Donald Tusk said on Tuesday peace could be achieved in Ukraine within weeks thanks to US security guarantees although success remained "far from 100 per cent certain".
Tusk also hinted at the possibility of US troops being sent to the line of contact between Ukraine and Russia, but he gave no details of such a proposal and the White House did not immediately comment on his remarks.
Amid the intensifying peace diplomacy, Russia launched more waves of drones against port infrastructure and civilian ships in Ukraine's Odesa region on Tuesday, Ukrainian navy and government officials said.
Odesa and the wider region nearby are home to the Black Sea ports that are crucial for Ukraine's foreign trade and the survival of its wartime economy.
