US President Donald Trump announced on Friday that he would meet his Russian counterpart, Vladimir Putin, in Alaska on August 15, saying the parties, including Zelenskiy, were close to a deal that could resolve the three-and-a-half-year conflict.
Details of the potential deal have yet to be announced, but Trump said it would involve "some swapping of territories to the betterment of both".
It could require Ukraine to surrender significant parts of its territory - an outcome Kyiv and its European allies say would only encourage Russian aggression.
"Ukrainians will not gift their land to the occupier," Zelenskiy said in a video address, adding that Ukraine's borders were fixed in the country's constitution.
"No one will deviate from this."
US Vice President JD Vance will meet Ukrainian and European allies in Britain on Saturday to discuss Trump's push for peace, Downing Street said, adding that British Prime Minister Keir Starmer had spoken about it with Zelenskiy.
"They agreed this would be a vital forum to discuss progress towards securing a just and lasting peace," the Downing Street spokesperson added.
Zelenskiy has made a flurry of calls with Ukraine's allies since Trump's envoy Steve Witkoff's visit to Moscow on Wednesday, which Trump described as having achieved "great progress".
"Clear steps are needed, as well as maximum coordination between us and our partners," Zelenskiy said in a post on X after his call with Starmer.
"We value the determination of the United Kingdom, the United States, and all our partners to end the war."
Ukraine and the European Union have pushed back on proposals that they view as ceding too much to Putin, whose troops invaded Ukraine in February 2022, citing what Moscow called threats to Russia's security from a Ukrainian pivot towards the West.
Kyiv and its Western allies say the invasion is an imperial-style land grab.
Moscow has previously claimed four Ukrainian regions – Luhansk, Donetsk, Zaporizhzhia and Kherson – as well as the Black Sea peninsula of Crimea, which was annexed in 2014.
Russian forces do not fully control all the territory in the four regions.
Russia is demanding that Ukraine pull out its troops from the parts of all four of them that it still controls.
Ukraine says its troops still have a small foothold in Russia's Kursk region, a year after its troops crossed the border to try to gain leverage in any negotiations.
Russia said it had expelled Ukrainian troops from Kursk in April.
Tatiana Stanovaya, a senior fellow at the Carnegie Russia Eurasia Centre, described the current peace push as "the first more or less realistic attempt to stop the war".
"At the same time, I remain extremely sceptical about the implementation of the agreements, even if a truce is reached for a while. And there is virtually no doubt that the new commitments could be devastating for Ukraine," she said.
Fierce fighting is raging along the more than 1000-kilometre front line along eastern and southern Ukraine, where Russian forces hold around a fifth of the country's territory.
Russian troops are slowly advancing in Ukraine's east, but their summer offensive has so far failed to achieve a major breakthrough, Ukrainian military analysts say.
"Not a single serviceman will agree to cede territory, to pull out troops from Ukrainian territories," Olesia Petritska, 51, told Reuters as she gestured to hundreds of small Ukrainian flags in the Kyiv central square commemorating fallen soldiers.
