The talks are part of a months-long push for peace from US President Donald Trump's administration that also included meetings with Ukrainian and European officials in Berlin earlier this week.
"The discussions are proceeding constructively. They began earlier and will continue today, and will also continue tomorrow," Kirill Dmitriev told reporters in Miami on Saturday.
Dmitriev met with US envoy Steve Witkoff and Trump's son-in-law Jared Kushner, Russian state news agency RIA Novosti reported.
Ukrainian President Volodymyr Zelenskiy wrote on Telegram on Sunday that diplomatic efforts were "moving forward quite quickly, and our team in Florida has been working with the American side".
Ukrainian negotiator Rustem Umerov said his team will hold another meeting with US officials later on Sunday.
"We are working constructively and substantively. We are counting on further progress and practical results," Umerov said on Telegram.
The Kremlin denied on Sunday that trilateral talks involving Ukraine, Russia and the US were under discussion, after Zelenskiy said on Saturday that the US had proposed the idea of three-way discussions.
"At present, no one has seriously discussed this initiative, and to my knowledge it is not being prepared," Russian President Vladimir Putin's foreign affairs adviser Yuri Ushakov said.
Trump has unleashed an extensive diplomatic push to end the war but his efforts have run into sharply conflicting demands by officials in Russia and Ukraine.
The French presidency on Sunday welcomed Putin's willingness to speak with President Emmanuel Macron, saying it would decide how to proceed "in the coming days".
"As soon as the prospect of a ceasefire and peace negotiations becomes clearer, it becomes useful again to speak with Putin," Macron's office said in a statement.
"It is welcome that the Kremlin publicly agrees to this approach."
The statement came after Kremlin spokesman Dmitry Peskov said Putin was open to holding talks with Macron if there was mutual political will.
Macron's office said any dialogue would aim "to contribute to a solid and lasting peace for Ukraine and Europe, in full transparency with President Zelenskiy and our European partners".
European Union leaders agreed on Friday to provide 90 billion euros ($A160 billion) to Ukraine to meet its military and economic needs for the next two years, although they failed to bridge differences with Belgium that would have allowed them to use frozen Russian assets to raise the funds.
Instead, they were borrowed from capital markets.
Ukrainian human rights ombudsman Dmytro Lubinets on Sunday accused Russian forces of forcibly removing about 50 Ukrainian civilians from the Ukrainian Sumy border region to Russian territory.
Writing on social media, he said that Russian forces illegally detained the residents in the village of Hrabovske on Thursday, before moving them to Russia on Saturday.
Lubinets said he contacted Russia's human rights commissioner, requesting information on the civilians' whereabouts and conditions, and demanding their immediate return to Ukraine.
with DPA and Reuters
