In a joint statement, the United States and Ukraine said they had drafted a "refined peace framework" after talks in Geneva on Sunday.
Although there were no specifics, the dialogue received a cautious welcome from some of Ukraine's allies.
Ukraine's delegation to the talks with US officials in Switzerland was returning home on Monday to report back, President Volodymyr Zelenskiy said.
US President Donald Trump hinted at new progress.
"Is it really possible that big progress is being made in Peace Talks between Russia and Ukraine??? Don't believe it until you see it, but something good just may be happening," Trump wrote on Truth Social.
A 28-point peace proposal caught many in the US government, Ukraine and European countries off-guard and prompted fresh concerns that the United States might be willing to push Ukraine to sign a peace deal heavily tilted towards Russia.
The plan would reportedly require Ukraine to cede some territory, accept curbs on its military size and bar it from joining the NATO military alliance.
Ukraine's European allies drew up a counter-proposal which, according to a copy reviewed by Reuters, would halt fighting at present front lines, leaving discussions of territory for later and include a NATO-style US security guarantee for Ukraine.
The sudden US push raises the pressure on Ukraine and Zelenskiy, who is at his most vulnerable since the start of the war after a corruption scandal resulted in two of his ministers being dismissed and as Russia makes battlefield gains.
After Sunday's talks, no public statement was released on how the revised plan would handle contentious issues such as how to guarantee Ukraine's security against future Russian threats or how to fund the rebuilding of Ukraine.
Some media reports said the initial US proposal would require frozen Russian assets to be pooled in an investment fund for Ukraine's reconstruction.
Zelenskiy said negotiations were ongoing.
"We all continue working with partners, especially the United States, to look for compromises that will strengthen but not weaken us," Zelenskiy said via video link from a separate meeting of Ukraine's allies in Sweden.
Zelenskiy could travel to the United States as soon as this week to discuss the most sensitive aspects of the plan with Trump, according to sources familiar with the matter.
Ukraine's second-largest city Kharkiv was hit by what officials said was a massive drone attack that killed four people on Sunday.
With smoke rising from the rubble, one man was seen crouched and holding the hand of a dead body.
"There was a family, there were children," said Ihor Klymenko, Red Cross Commander of the emergency-response team in Kharkiv.
"I can't tell you how, but the children are alive, thank God, the man is alive. The woman died, unfortunately."
Across the border, Russian air defences shot down 10 drones en route to Moscow on Monday, the Defence Ministry said.
From 8am to 8pm, 50 Ukrainian drones were downed across the Moscow, Bryansk, Kaluga and Kursk regions as well as Crimea and over the waters of the Black Sea, the ministry said in a statement.
Moscow Mayor Sergei Sobyanin said emergency services were working at sites where debris from drones bound for the capital had fallen.
