However, Kremlin spokesman Dmitry Peskov played down any perception of progress, denying there had been a breakthrough, in a report from the Izvestia news outlet
"This is a working process," Peskov said, when asked whether the negotiations that took place in Miami on December 20-21 could be seen as a turning point.
Ukrainian negotiators led by senior official Rustem Umerov, along with representatives from Europe, have held a series of meetings with US envoys, including in recent days in Florida.
Russian negotiator Kirill Dmitriev, President Vladimir Putin's investment envoy, has also been holding separate talks with US officials in Florida.
Officials in both Ukraine and Russia said their teams were returning home on Monday to report on the outcome of the discussions.
"It all looks quite worthy ... And here it is important that this is the work of both us (Ukraine) and the United States of America. This suggests that we are very close to a real result," Zelenskiy told a gathering devoted to Ukrainian diplomats.
Zelenskiy said the negotiators had been working on a 20-point plan, put forward by US envoys, which has been under discussion for weeks after an initial draft was criticised by Ukrainians and Europeans as being too slanted towards Russia.
"Not everything is ideal with this, but the plan is there," he said.
Also under discussion were security guarantees Ukraine has been seeking to guard against any future Russian military action once the fighting stops, as well as a plan for Ukraine's economic recovery.
"The basic block of all the documents is ready. It's basic," Zelenskiy said.
"There are some matters for which we are not prepared. And I am certain that there are matters for which the Russians are not prepared."
The US team has been led by President Donald Trump's envoy, Steve Witkoff, and his son-in-law, Jared Kushner.
Speaking later in his nightly video address, Zelenskiy said the key issue was to determine whether the United States was able to "get a response from Russia, real readiness on the part of that country to focus on something other than aggression".
He said continued pressure on the Kremlin was vital to reduce Moscow's capacity to wage war.
"Lowering the price of Russian oil, strong global sanctions and continued other forms of pressure are what can persuade even a stubborn person," he said.
"This year, much has already been done to reduce the money available to Russia's war machine."
Meanwhile, Russian forces struck Ukraine's Black Sea port of Odesa late on Monday and damaged port facilities and a ship, the second attack on the region in less than 24 hours.
Governor Oleh Kiper, writing on Telegram, said emergency crews were tackling the aftermath of the latest attack but provided no further details.
An earlier overnight attack hit port and energy infrastructure in Odesa region, causing a fire at a major port and disrupting electricity supplies to tens of thousands of people.
Ukraine's Black Sea ports are crucial for its export-driven economy and their security and functionality have been vital for the country's economic survival throughout nearly four years of war in Ukraine since Russia's invasion in February 2022.
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