US President Donald Trump said "a lot of progress" was made during talks with Ukrainian President Volodymyr Zelensky at his Mar-a-Lago estate in Florida today. However, "one or two thorny issues" remain.
"We're getting a lot closer, maybe very close" to ending the conflict, Mr Trump told reporters.
He said they discussed a lot of points and are "getting a lot closer".
The US president said the pair also held a phone call with European and world leaders.
"We have made a lot of progress on ending that war," Mr Trump said.
"We discussed all the aspects of the peace framework," Mr Zelensky said, adding that it is 90% agreed.
He said that the security guarantees are 100% agreed, while US-Europe security guarantees are almost agreed with the military dimension 100% agreed.
He said the prosperity plan is being finalised. He added that security guarantees are the "key milestone in achieving lasting peace".
"Our teams will continue working on all aspects," Mr Zelensky added.
Watch: We've made a lot of progress, says Trump
Earlier, Mr Zelensky had said he hoped to soften a US proposal for Ukrainian forces to withdraw completely from the Donbas region of eastern Ukraine, a Russian demand that would mean ceding some territory held by Ukrainian forces.
When asked at the press conference after today's talks if Russia has been asking Ukraine to give up Donbas, Mr Trump said it is an issue they have to "iron out". "But I think they are moving in the right direction," he said.
Just before Mr Zelensky and his delegation arrived in Florida, the US and Russian presidents spoke in a call described as "productive" by Mr Trump and "friendly" by Kremlin foreign policy aide Yuri Ushakov.
Mr Ushakov, in Moscow, said Mr Putin told Mr Trump a 60-day ceasefire proposed by the European Union and Ukraine would prolong the war. The Kremlin aide also said Ukraine needs to make a quick decision about land in the Donbas.
Watch: 'One or two thorny issues' remain, says Trump
Mr Zelensky arrived at Mar-a-Lago this afternoon, as Russian air raids pile pressure on Kyiv. Russia hit the capital and other parts of Ukraine with hundreds of missiles and drones yesterday, knocking out power and heat in parts of Kyiv.
Mr Zelensky has described the weekend attacks as Russia's response to the US-brokered peace efforts, but today Mr Trump said he believes Mr Putin and Mr Zelensky are serious about peace.
"I do think we have the makings of a deal," Mr Trump said.
"We have two willing countries. We are in the final stages of talking," he said.
The US president said he would call Mr Putin again after meeting with Mr Zelensky.
Russia claims more battlefield advances
Moscow has repeatedly insisted that Ukraine yield all of the Donbas, even areas still under Kyiv's control, and Russian officials have objected to other parts of the latest proposal, sparking doubts about whether Mr Putin would accept whatever today's talks might produce.
Mr Putin said yesterday that Moscow would continue waging its war if Kyiv did not seek a quick peace.
Russia has steadily advanced on the battlefield in recent months, claiming control over several more settlements today. A recent poll suggests Ukrainian voters may reject the plan.
Mr Zelensky's in-person meeting with Mr Trump followed weeks of diplomatic efforts. European allies, while at times cut out of the loop, have stepped up efforts to sketch out the contours of a post-war security guarantee for Kyiv that the United States would support.
Read More: The 20-point peace proposal Zelensky will discuss with Trump
Today, ahead of his meeting with Mr Trump, Mr Zelensky said he held a detailed phone call with British Prime Minister Keir Starmer.
Kyiv and Washington have agreed on many issues, and Mr Zelensky said on Friday that the 20-point plan was 90% finished. But the issue of what territory, if any, will be ceded to Russia remains unresolved.
While Moscow insists on getting all of the Donbas, Kyiv wants the map frozen at current battle lines.
The United States, seeking a compromise, has proposed a free economic zone if Ukraine leaves the area, although it remains unclear how that zone would function in practical terms.
It has also proposed shared control over the Zaporizhzhia nuclear power plant, where power line repairs have begun after another local ceasefire brokered by the International Atomic Energy Agency, the agency said today.
Mr Zelensky, whose past meetings with Mr Trump have not always gone smoothly, worries along with his European allies that Mr Trump could sell out Ukraine and leave European powers to foot the bill for supporting a devastated nation, after Russian forces took 12 to 17 sq/km (4.6-6.6 square miles) of its territory per day in 2025.
Russia controls all of Crimea, which it annexed in 2014, and since its invasion of Ukraine nearly four years ago has taken control of about 12% of its territory, including about 90% of Donbas, 75% of the Zaporizhzhia and Kherson regions, and slivers of the Kharkiv, Sumy, Mykolaiv and Dnipropetrovsk regions, according to Russian estimates.
On 19 December, Mr Putin said that a peace deal should be based on conditions he set out in 2024: Ukraine withdrawing from all of the Donbas, Zaporizhzhia and Kherson regions, and Kyiv officially renouncing its aim to join NATO.
Ukrainian officials and European leaders view the war as an imperial-style land grab by Moscow and have warned that if Russia gets its way with Ukraine, it will one day attack NATO members.
The 20-point plan was spun off from a Russian-led 28-point plan, which emerged from talks between US special envoy Steve Witkoff, Mr Trump's son-in-law Jared Kushner and Russian special envoy Kirill Dmitriev, and which became public in November.
Subsequent talks between Ukrainian officials and US negotiators have produced the more Kyiv-friendly 20-point plan.
