Senior Ukrainian and US negotiators have jointly called on Russia to show a "serious commitment to long-term peace" after talks in Moscow earlier this week failed to produce a breakthrough.
US special envoy Steve Witkoff and Rustem Umerov, secretary of Ukraine's national security council, have held two days of what a statement described as "constructive discussions" in Florida.
The prospect of ending the war in Ukraine depended on Russia's readiness to take "steps towards de-escalation and cessation of killing", the statement said.
The negotiations, which are also attended by US President Donald Trump's son-in-law Jared Kushner, will continue for a third day on Saturday.
During the talks, Witkoff and Umerov "agreed on the framework of security arrangements" that could accompany a peace agreement and "discussed necessary deterrence capabilities to sustain a lasting peace", the statement said without giving further details.
The Florida talks saw Ukraine's team briefed on the meeting between Trump's most senior overseas envoy and Russian President Vladimir Putin earlier this week.
Witkoff spent almost five hours with Putin in Moscow on Tuesday, after which the Kremlin said "no compromise" had been reached on the draft US peace plan.
The Kremlin said Putin was ready to continue meeting the Americans "as many times as needed", but Ukraine and its allies in Europe have called into question the Russian leader's commitment to ending the war.
On Friday, Ukrainian President Volodymyr Zelensky said he wanted to "obtain full information about what was said in Moscow and what other pretexts Putin has come up with to drag out the war".
Kyiv pushed for revisions to the US peace plan, which was widely seen as favourable to Moscow when an initial version leaked to the media. It has since undergone several changes, though a more recent version has not been shared publicly.
Major points of contention remain between the two sides, including security guarantees for Ukraine post-war and territorial concessions.
Russia currently controls roughly one-fifth of Ukraine's territory, including swathes of the Donbas area in the east – made up of the Donetsk and Luhansk regions.
In an interview with India Today on Friday, Putin warned Ukrainian troops to withdraw fully from the region this week, saying Russia would otherwise "liberate these [Donbas] territories by force".
Ahead of the US visit to the Kremlin, Putin was filmed in army fatigues at a Russian command post, being briefed by commanders claiming they had captured the strategic city of Pokrovsk, in the Donetsk region, as well as other nearby settlements.
Ukraine rejects Russia's claim that it has lost control of the city.
Kyiv and its European allies believe the most effective way to deter Russia from attacking again in the future would be to grant Ukraine membership of Nato, or to provide comprehensive security guarantees.
Russia is staunchly opposed, while Trump too has repeatedly signalled he has no intention of letting Ukraine join the military alliance.
The prospect of Ukraine joining Nato was a "key question" that was tackled in Moscow, the Kremlin said on Wednesday.
Trump said those talks were "reasonably good", but it was too soon to say what would happen. He said it was too soon to say what would happen as "it does take two to tango".
