In his latest abrupt pivot on Russia's 2022 invasion, Trump said he expected to meet Putin in Budapest within the next two weeks for what would be their second summit since the American's return to power.
The Kremlin welcomed the "extremely frank and trustful" call and said it was immediately preparing for the summit.
Ukraine's President Volodymyr Zelensky insisted that the threat of Tomahawks had pushed Moscow to negotiate, even as he deals with yet another Trump shift on the war.
"I believe great progress was made with today's telephone conversation," Trump said on his Truth Social network, saying he and Putin would meet to "see if we can bring this 'inglorious' War, between Russia and Ukraine, to an end."
The 79-year-old Republican later told reporters in the Oval Office that the call was "very productive" and that he expected to meet "within two weeks or so, pretty quick."
US Secretary of State Marco Rubio will swiftly meet his Russian counterpart Sergei Lavrov to sort out summit details, Trump added.
- 'Momentum' -
Trump said the Russian leader "didn't like it" when he raised the possibility during their call of giving Moscow's enemy Ukraine the missiles with a 1,000-mile (1,600-kilometer) range.
But Trump appeared to cast doubt on whether Ukraine would actually get the American-made arms it covets, saying the United States could not "deplete" its own supply.
"We need them too, so I don't know what we can do about that," he said.
Trump's relations with Putin -- a leader for whom he has repeatedly expressed admiration over the years -- have blown hot and cold since he returned to the White House in January.
After an initial rapprochement, Trump has shown increasing frustration, particularly since he came away from Alaska with no end to the war he once promised to solve within 24 hours.
Zelensky meanwhile has gone the opposite way, winning Trump's support after a disastrous initial meeting in February when the US president berated him in front of the cameras.
But Trump's latest swing appears to have moved the dial again, leaving Zelensky having to negotiate the situation with Ukraine's main military backer.
Zelensky said as he arrived Thursday in Washington that he hopes the "momentum" of the Middle East peace deal Trump brokered will help end the war in Ukraine.
"We can already see that Moscow is rushing to resume dialogue as soon as it hears about Tomahawks," Zelensky said, adding that he'll also be meeting US defence companies to discuss additional supplies of air defence systems.
- 'Peace summit' -
The Kremlin hailed the "highly substantive" Putin-Trump call, which Putin's top aide Yuri Ushakov told journalists was at Russia's initiative.
But Putin told Trump that giving Ukraine Tomahawks would "not change the situation on the battlefield" and would harm "prospects for peaceful resolution," added Ushakov.
Budapest had been discussed as a possible venue for the previous Trump-Putin meeting before they settled on Alaska.
Hungarian Prime Minister Viktor Orban, who has maintained friendly relations with both men, said later that he had spoken to Trump. "Preparations for the USA-Russia peace summit are underway," he said on X.
The choice of Budapest also sidesteps an International Criminal Court arrest warrant for Putin for alleged war crimes.
Hungary has announced its withdrawal from the ICC yet is still theoretically a member until June 2026.
But Orban gave Israeli Prime Minister Benjamin Netanyahu a promise that he would not carry out the warrant when Netanyahu visited Hungary in April.
In Ukraine the war ground on with Moscow renewing its attacks on Kyiv's energy grid.
Russian strikes forced Ukraine to introduce nationwide rolling power cuts, for the second day in a row, in the cold season when temperatures can fall to zero at night.
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