AFPUS envoy Steve Witkoff and Russian President Vladimir Putin had "constructive" talks in Moscow on Friday lasting three hours, according to an aide of Putin's.
Yuri Ushakov said the possibility of Russia and Ukraine resuming direct talks was a particular point of discussion.
The US has not released details of what was discussed during the meeting, but as it took place US President Donald Trump hinted the two sides were close to reaching a deal.
Meanwhile, Ukrainian President Volodymyr Zelensky urged allies to apply more pressure on Russia, blaming Moscow for failing to agree to a previous temporary ceasefire presented by the US.
Traffic was halted as a convoy of cars carrying Witkoff arrived in central Moscow, as he made his fourth visit to Russia since the start of the year.
The three-hour talks were described as "constructive and very useful" by Putin aide Ushakov.
It had brought the "Russian and US positions closer together not just on Ukraine but also on a range of other international issues", he said.
"Specifically on the Ukrainian crisis, the possibility of resuming direct talks between Russian and Ukrainian representatives was in particular discussed," he added.
Earlier this week, Putin signalled for the first time since the early stages of the war that he was open to talks with Zelensky.
His remarks were believed to be in response to a proposal by the Ukrainian president for the 30-hour Easter truce to be extended for 30 days. No truce has yet been agreed on.
Kyiv has been on the receiving end of growing pressure from Trump to accept territorial concessions as part of an agreement with Moscow to end the war.
The issue of the occupied Crimean peninsula, which was illegally annexed by Russia in 2014, has become a particular flashpoint.
Zelensky has repeatedly rejected the idea of recognising Crimea as part of Russia, telling reporters in Kyiv on Friday: "Our position is unchanged - only the Ukrainian people have the right to decide which territories are Ukrainian."
However, in later remarks he suggested "territorial issues" could be discussed if a "full and unconditional ceasefire" is agreed on.
"A full and unconditional ceasefire opens up the possibility to discuss everything," he said.
He also referenced comments made by Trump in an interview with Time magazine, in which the US president said "Crimea will stay with Russia".
"What President Trump says is true, and I agree with him in that today we do not have enough weapons to return control over the Crimean peninsula," Zelensky said.
The US's peace plan has not been publicly released, but reports suggest it proposes Russia keeps the land it has gained, amounting to about 20% of Ukraine's territory - a condition that is in Moscow's favour.
According to the Reuters news agency, which has seen US proposals handed to European officials last week as well as subsequent counter-proposals from Europe and Ukraine, there are significant disparities between them.
The US deal offers American legal acceptance of Russia's illegal annexation of Crimea and de facto recognition of Russian control of other occupied areas, including all of the Luhansk region.
By contrast, the Europeans and Ukrainians will only discuss what happens to occupied Ukrainian territory after a ceasefire has come into effect.
As the meeting between Witkoff and Putin was taking place, Trump claimed talks were going in the right direction.
"They're meeting with Putin right now, as we speak, and we have a lot of things going on, and I think in the end we're going to end up with a lot of good deals, including tariff deals and trade deals," he told reporters in the US.
He said his aim was to bring about an end to fighting in Ukraine which was claiming the lives of 5,000 Ukrainian and Russians a week, adding he believed "we're pretty close" to a peace deal.
But Russia and Ukraine's positions still seem miles apart, with no representative from Ukraine invited to take part in the talks in Moscow.
Writing on social media on Friday, Zelensky criticised Russia for failing to agree to a 30-day ceasefire proposed by the US on 11 March and urged allies to apply more pressure to it.
"It's been 45 days since Ukraine agreed to President Trump's proposal for quiet in the sky, sea and the frontline," he said. "Russia rejects all this. Without pressure this cannot be resolved. Pressure on Russia is necessary."
He said Russia was being allowed to import missiles from countries such as North Korea, which he said it then used in a deadly missile strike on Kyiv on Thursday, which killed 12 people.
"Insufficient pressure on North Korea and its allies allows them to make such ballistic missiles. The missile that killed the Kyiv residents contained at least 116 parts imported from other countries, and most of them, unfortunately, were made by US companies," Zelensky alleged.
Following the attack on Kyiv, Trump said he was "putting a lot of pressure" on both sides to end the war, and directly addressed Putin in a post on social media, saying: "Vladimir STOP!"
Since then, however, Trump has blamed Kyiv for starting the war, telling Time magazine: "I think what caused the war to start was when they [Ukraine] started talking about joining Nato."
Ahead of the talks between Witkoff and Putin on Friday, a senior Russian general was killed in a car bomb attack in the Russian capital. The Kremlin accused Ukraine of being responsible. Kyiv has not commented.
Two people were also killed in a Ukrainian strike on the Russian region of Belgorod, the local governor said. Again, Ukraine has not commented on the claim.
