President Volodymyr Zelensky, who is in Copenhagen and in constant contact with Ukraine’s negotiating team, said Wednesday would be the main day of the talks.
The agenda includes de-escalation, in particular attacks on energy infrastructure and the situation in the Black Sea.
On Tuesday, the sides discussed a prisoner exchange of 1,000 for 1,000, Zelensky said, while Russia raised territorial issues.
The main point of dispute remains the Ukrainian land that Moscow lays claim to.
Zelensky described the first day as "constructive and quite substantive," saying security guarantees for his country were also discussed.
Jared Kushner, son-in-law of US President Donald Trump, who is leading the American side of the talks with envoy Steve Witkoff, wrote on X that he was "encouraged" by the discussions.
He said work was under way on security arrangements for Ukraine and Europe, and that Trump believed the war had gone on far too long.
The negotiations resume a process that has been on hold since February, when the US and Israel went to war with Iran.
Despite the positive signals, Ukrainian expectations remain low, according to analysts.
Oleksandr Khara of the Centre for Defence Strategies in Kyiv said he did not expect concrete results, because the compromise Washington is seeking is not currently possible.
In his view, the outcome depends on Russia's ability to keep fighting, not on Ukrainian goodwill.
He said Moscow still believes it can force a deal by attacking Ukraine's power system as winter approaches, but damage to Russia's own oil sector might push it to consider a temporary ceasefire on energy targets.
Ukraine and its European allies are also uneasy that Russia wants to discuss the security of the whole continent, not just the war.
Zelensky said Ukraine did not want a "Yalta 2.0" – a reference to the 1945 deal between the great powers, or for Russia to divide Europe.
American daily The Washington Post argued that Moscow had already scored a strategic success by drawing Washington into that wider debate.
Ukrainian analysts were less alarmed, with Vitaly Yarmolenko of the National Institute for Strategic Studies saying such Russian proposals were unlikely to win broad support.
Before the talks began, US and Ukrainian delegations met representatives of France, Germany, Italy, the UK, the EU and NATO.
Kushner and Witkoff said the meeting looked at building on existing European security institutions once the war ends, adding that NATO would remain central to collective defence.
The EU said "any future arrangements must respect sovereignty, territorial integrity, independent decision-making, and provide credible security guarantees for Ukraine."
Attention is also turning to the APEC summit in Shenzhen on 17-18 November, where the Kremlin says Trump, Russia's Vladimir Putin and China's Xi Jinping could discuss the war and European security.
Neither Washington nor Beijing has confirmed such a meeting.
Khara said any decisions taken without Europe and Ukraine would carry little weight.
(ał)
Source: PAP, IAR