Zelenskiy said he held a "long and substantive" conversation with Trump on Saturday after the US leader met Putin in Alaska.
He thanked Trump for an invitation to meet in person in Washington on Monday and said they would "discuss all of the details regarding ending the killing and the war".
Zelenskiy reiterated the importance of involving Europe.
"It is important that Europeans are involved at every stage to ensure reliable security guarantees together with America," he said.
"We also discussed positive signals from the American side regarding participation in guaranteeing Ukraine's security."
Zelenskiy said he spoke to Trump one-on-one and then in a call with other European leaders.
In total the conversations lasted an hour and a half.
Trump rolled out the red carpet for Putin in Alaska, but Friday's summit appeared to end without concrete progress on bringing an end to the war.
Trump said "there's no deal until there's a deal" after Putin claimed the two leaders had hammered out an "understanding" on Ukraine and warned Europe not to "torpedo the nascent progress".
During an interview with Fox News Channel before leaving Alaska, Trump insisted that the onus going forward might be on Zelenskiy "to get it done", but said there would also be some involvement from European nations.
Trump did not speak to reporters on his flight back to Washington.
When his plane landed, White House press secretary Karoline Leavitt told reporters that Trump was on the phone with NATO leaders after a lengthy call with Zelenskiy.
Trump then disembarked Air Force One without speaking to reporters. He did not respond to shouted questions about the phone calls as he climbed into his limousine.
Trump spoke with Zelenskiy, German Chancellor Friedrich Merz, French President Emmanuel Macron, British Prime Minister Keir Starmer, Italian Premier Giorgia Meloni, Finnish President Alexander Stubb, Polish President Karol Nawrocki, European Commission President Ursula von der Leyen and NATO Secretary-General Mark Rutte, European Commission spokesperson Arianna Podesta said.
She gave no details of the conversation.
There was no immediate comment on Saturday from European leaders who, like Zelenskiy, did not have a place at the table at Friday's summit.
Putin's foreign affairs adviser, Yuri Ushakov, said on Russian state television Saturday that a potential trilateral meeting between Trump, Putin and Zelenskiy has not been raised in US-Russia discussions.
"The topic has not been touched upon yet," Ushakov said, according to Russian state news agency RIA Novosti.
Russian attacks on Ukraine continued overnight, using one ballistic missile and 85 Shahed drones, 61 of which were shot down, Ukraine's Air Force said.
Frontline areas of Sumy, Dnipropetrovsk, Donetsk and Chernihiv were attacked.
