Secretary of State Marco Rubio described the US-brokered meeting on Tuesday as very productive, without giving details.
Ukrainian President Volodymyr Zelenskiy called the talks "constructive and quite substantive", and said they had included humanitarian and security issues.
Addressing reporters later in Denmark, Zelenskiy said he was pleased with messages he had been receiving from the two US envoys, Steve Witkoff and Jared Kushner.
"I see changes. I am very happy about what I hear," Zelenskiy said.
"The release of prisoners (of war) is a priority. They spoke in detail about the substance of security guarantees for Ukraine and the foundations for ensuring these guarantees function over the long term," he posted on X.
The meeting followed US contacts with both sides in recent weeks that Kushner said had narrowed gaps between their positions.
"We are encouraged by the constructive discussions today," Kushner wrote on X after the first day wrapped up.
He said the US side was working to end the war and "establish the security arrangements necessary for a sovereign, secure, and prosperous Ukraine and lasting peace across Europe."
The warring sides remain far apart on terms for a possible settlement, more than four-and-a-half years after Russia's full-scale invasion of Ukraine.
Russian forces control about a fifth of Ukraine, but territory is not the only issue at stake. Others include future security guarantees, which both sides want, and Moscow's demands that Ukraine adopt neutral status and not join NATO.
Trump has intensified pressure on Kyiv to reach a deal, saying it is time for Ukraine to end the war or face "a very bad thing". Last week he said the war was close to being settled in a "big beautiful agreement", but he has frequently predicted breakthroughs that have not materialised.
Russian Foreign Minister Sergei Lavrov underlined Moscow's preference for negotiating a broad European security framework before tackling the specifics of the war.
"The idea of defining clear parameters for a future security architecture, and only then moving on to resolving the actual Russia-Ukraine conflict, is absolutely reasonable," he said in Moscow.
Zelenskiy told journalists he had deep reservations about the proposals for a new security architecture.
"Everybody is ready for dialogue. First, stop the war in Ukraine. Second, security guarantees for Ukraine. Third, maybe some dialogue about the topic of security in Europe, in the world."
European Commission President Ursula von der Leyen said on Monday wider security talks should only follow a ceasefire. Lavrov rejected the notion of a truce, saying the Europeans were trying to secure breathing space for Ukraine.
