Trump announced on Friday that he would meet Putin in Alaska on August 15, saying the parties, including Ukrainian President Volodymyr 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.
US Vice President JD Vance met Ukrainian and European allies in Britain on Saturday at Chevening House, a country mansion southeast of London, to discuss Trump's push for peace.
The Wall Street Journal said European officials had presented a counter-proposal, including demands that a cease-fire must take place before any other steps are taken and that any territory exchange must be reciprocal, with firm security guarantees.
"You can't start a process by ceding territory in the middle of fighting," it quoted one European negotiator as saying.
A US official said "hours-long" meetings at Chevening "produced significant progress toward President Trump's goal of bringing an end to the war in Ukraine. The White House did not immediately respond when asked if the Europeans had presented their counter-proposals to the US
British Prime Minister Keir Starmer and French President Emmanuel Macron spoke and pledged to find a "just and lasting peace" in Ukraine, a Downing Street spokesperson said.
"They discussed the latest developments in Ukraine, reiterating their unwavering support to President Zelenskiy and to securing a just and lasting peace for the Ukrainian people."
"They welcomed President Trump's efforts to stop the killing in Ukraine and end Russia's war of aggression, and discussed how to further work closely with President Trump and President Zelenskiy over the coming days."
Zelenskiy said the meeting was constructive.
"The path to peace for Ukraine should be determined together and only together with Ukraine, this is key principle," he said.
He had earlier rejected any territorial concessions, saying: "Ukrainians will not give their land to the occupier".
Macron also said Ukraine must play a role in any negotiations.
"Ukraine's future cannot be decided without the Ukrainians, who have been fighting for their freedom and security for over three years now," he wrote on X after what he said were calls with Zelenskiy, German Chancellor Friedrich Merz and British Prime Minister Keir Starmer.
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".
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.
