US President Donald Trump has said Russia and Ukraine “are very close to a deal”, hours after his envoy Steve Witkoff and Russian President Vladimir Putin held talks in Moscow.

Trump said it had been a “good day” of negotiations, while the Kremlin described the talks – which Ukraine was not present at – as “constructive”.

Earlier, Trump said on social media that “most of the major points are agreed to,” and urged Russia and Ukraine to meet “at very high levels” and “to finish it [the deal] off”.

Meanwhile, Ukrainian President Volodymyr Zelensky said in his video address late on Friday that “real pressure on Russia is needed” to accept an unconditional ceasefire.

Earlier in the day, Zelensky told the BBC that territorial issues between Kyiv and Moscow could be discussed if a “full and unconditional ceasefire” was agreed upon.

Reports suggest Ukraine would be expected to give up large portions of land annexed by Russia under a US peace proposal.

Trump – who spoke to reporters as he arrived in Rome for Saturday’s funeral of Pope Francis – has said he would support Russia keeping the Crimean peninsula, which was illegally annexed by Moscow in 2014. Zelensky rejects this idea.

Russia launched a full-scale invasion of Ukraine in 2022, and Moscow currently controls almost 20% of Ukrainian territory.

On Friday, traffic was halted in Moscow as a convoy of cars carrying Witkoff arrived ahead of the high-level talks, the fourth such visit he has made to Russia since the start of the year.

The three-hour talks were described as “very useful” by Putin aide Yuri 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 a 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.

Crimea has become a particular flashpoint.

Zelensky has repeatedly rejected the idea of recognising the peninsula 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 to the BBC that “a full and unconditional ceasefire opens up the possibility to discuss everything”.

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.

Washington’s peace plan has not been publicly released, but reports suggest it proposes Russia keeps the land it has gained – a condition that is in Moscow’s favour.

On Friday, Reuters news agency reported it had seen US proposals handed to European officials last week, as well as subsequent counter-proposals from Europe and Ukraine.

It said 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.

The US plan also rules out Ukraine’s membership in the Nato military alliance, according to Reuters.

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 he said was claiming the lives of 5,000 Ukrainian and Russians a week, adding he believed “we’re pretty close” to a peace deal.

Trump also said Zelensky had not signed the “final papers on the very important Rare Earths Deal with the United States”.

“It is at least three weeks late,” he said, adding that he hoped it would be signed “immediately”.

The long-talked of minerals deal, which would give the US a stake in Ukraine’s abundant natural resource deposits, was meant to be signed in February but was derailed after an acrimonious meeting between Trump and Zelensky in Washington.

Russia and Ukraine’s positions in securing a peace deal 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 and injured dozens.

“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.”