The meeting next Friday is a potential major milestone after expressing weeks of frustration that more was not being done to quell the fighting.
Trump made the announcement on social media after he said that the parties, including Ukraine President Volodymyr Zelenskiy, were close to a ceasefire deal that could resolve the three-and-a-half-year conflict, one that could require Ukraine to surrender significant territory.
Addressing reporters at the White House earlier on Friday, Trump suggested an agreement would involve some exchange of land.
"There'll be some swapping of territories to the betterment of both," the Republican president said.
However, Zelenskiy said on Saturday that Ukraine could not violate its constitution on the territorial issues, adding "Ukrainians will not gift their land to the occupiers".
The Kremlin confirmed the summit in an online statement.
The two leaders would "focus on discussing options for achieving a long-term peaceful resolution to the Ukrainian crisis", Putin aide Yuri Ushakov said.
"This will evidently be a challenging process, but we will engage in it actively and energetically," Ushakov said.
In a video address to the nation posted on social media on Saturday, Zelenskiy said any decisions without Ukraine would be decisions against peace.
"They will not achieve anything. These are stillborn decisions. They are unworkable decisions. And we all need real and genuine peace," Zelenskiy said.
Putin claims four Ukrainian regions - Luhansk, Donetsk, Zaporizhzhia and Kherson - as well as the Black Sea peninsula of Crimea, which he annexed in 2014. His forces do not fully control all the territory in the four regions.
Ukraine has previously signaled a willingness to be flexible in the search for an end to a war that has ravaged its towns and cities and killed large numbers of its soldiers and citizens.
But accepting the loss of around a fifth of Ukraine's territory would be painful and politically challenging for Zelenskiy and his government.
Since his return to the White House in January, Trump has moved to mend relations with Russia and sought to end the war. In his public comments he has veered between admiration and sharp criticism of Putin.
In a sign of his growing frustration with Putin's refusal to halt Russia's military offensive, Trump had threatened to impose new sanctions and tariffs from Friday against Moscow and countries that buy its exports unless the Russian leader agreed to end the conflict, the deadliest in Europe since World War Two.
It was unclear by Friday evening whether those sanctions would take effect or be delayed or cancelled.
The administration took a step toward punishing Moscow's oil customers on Wednesday, imposing an additional 25 per cent tariff on goods from India over its imports of Russian oil, marking the first financial penalty aimed at Russia in Trump's second term.
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