Ukraine's President Volodymyr Zelensky said trilateral talks between Ukraine, Russia and the United States, which had concluded in the UAE, were "constructive" and that further meetings could take place next week.
Mr Zelensky said military representatives had identified a list of issues for discussion at a potential future meeting.
A UAE government spokesperson said the talks in Abu Dhabi focused on the "outstanding elements" of the US-proposed peace framework.
They said the talks included "direct engagement" between officials from both countries and were held in a "constructive and positive atmosphere".
Earlier, Ukraine's top negotiator Rustem Umerov said discussions would focus "on the parameters for ending Russia's war and the further logic of the negotiation process".
An initial US draft drew heavy criticism in Ukraine and western Europe for siding too closely to Russia's line, while later iterations prompted pushback from Russia for floating the idea of European peacekeepers.
Both sides say the fate of territory in the eastern Donbas region is one of the main outstanding issues in the search for a settlement to a war that has killed tens of thousands, displaced millions and decimated parts of Ukraine.
President Trump met Ukrainian President Volodymyr Zelensky at the World Economic Forum in Davos on Thursday and US envoy Steve Witkoff later held talks with Russian President Vladimir Putin in the Kremlin.
Thousands of people in Kyiv were without heating in sub-zero temperatures due to Russian strikes.
The European Union, which has sent hundreds of generators, accused Russia of "deliberately depriving civilians of heat".
Further Russian strikes killed one person and injured 22 others in Ukraine's capital and the northeastern city of Kharkiv overnight, authorities said.
While diplomacy to end Europe's worst conflict since World War II has gained pace, Russia and Ukraine appear deadlocked over the issue of territory.
Hours after Mr Putin met Mr Witkoff, and Mr Trump's son-in-law Jared Kushner, in Moscow, the Kremlin said its demand that Ukraine withdraw from the eastern Donbas region still stood.
"Russia's position is well known on the fact that Ukraine, Ukrainian armed forces, have to leave the territory of the Donbas," Kremlin spokesperson Dmitry Peskov said.
"This is a very important condition," he added.
Ukraine, which still controls around 20% of the eastern region, has rejected such terms.
Ahead of the talks yesterday, Mr Zelensky told reporters territory remained a "key issue" - with Russia having said it is not dropping its demand that Ukraine pull out of its eastern Donbas region.
In a post online, he later added: "It is necessary that not only Ukraine has the desire to end the war and achieve full security, but that a similar desire somehow emerges in Russia as well."
Mr Putin has repeatedly said Moscow intends to get full control of eastern Ukraine by force if talks fail.
After the Russia-US talks in the Kremlin, Putin aide Yuri Ushakov insisted Moscow was "genuinely interested in resolving" the war diplomatically.
But he added: "Until that happens, Russia will continue to achieve its objectives ... on the battlefield."
Mr Trump has in the past pressured Ukraine to agree to terms that Kyiv sees as capitulation.
He repeated on Wednesday his belief that Mr Putin and Mr Zelensky were close to a deal.
"I believe they're at a point now where they can come together and get a deal done. And if they don't, they're stupid - that goes for both of them," he said.
