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 - which, like the Ukrainian leader, was not at the table at Friday's summit.
"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."
He did not elaborate, but Zelenskiy previously has said European partners put on hold a proposal to establish a foreign troop presence in Ukraine as a deterrence against future Russian aggression because it lacked an American backstop.
Zelenskiy said he spoke to Trump one-on-one and then in a call with other European leaders, with the conversations in total lasting more than 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.
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.
Zelenskiy voiced support for Trump's proposal for a trilateral meeting with the US and Russia.
He said "key issues can be discussed at the level of leaders, and a trilateral format is suitable for this".
But Putin's foreign affairs adviser, Yuri Ushakov, said on Russian state television on 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 officials and media struck a largely positive tone, with some describing Friday's meeting as a symbolic end to Putin's isolation in the West.
Russia's former President Dmitry Medvedev, deputy head of the country's Security Council, praised the Alaska summit as a breakthrough in restoring high-level dialogue between Moscow and Washington, describing the talks as "calm, without ultimatums and threats".
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.
