"There is no encirclement of our troops," Zelenskiy wrote on X, confirming what the Kiev General Staff said on Friday.
Speaking to journalists in Kyiv on Saturday, Zelenskiy called the alleged encirclement a "lie by Putin".
He did not rule out the possibility that Russia could attempt to encircle Kyiv units near the border on Ukrainian territory.
Earlier, Kremlin spokesman Dmitry Peskov told the Russian state news agency TASS that time was running out for the Ukrainian forces fighting in Kursk.
He added that the offer to spare the lives of Ukrainian troops still stands but would not last indefinitely.
US President Donald Trump had asked Russian President Vladimir Putin to spare the lives of Ukrainian soldiers said to be surrounded in Kursk.
Putin agreed, but demanded that the leadership in Kyiv order the Ukrainian soldiers in the region to lay down their weapons and surrender.
Zelenskiy had previously indicated that his army would have to withdraw from the region, saying "I can only thank our fighters for this operation, which has fulfilled its task".
He now says operations continue in designated areas of Kursk and troops are carrying out their tasks as required.
He wrote that thanks to the soldiers there, a considerable number of Russian forces had withdrawn from other areas.
Ukraine took the war into Russian territory in a surprise attack last August.
The original justification for the move was to be able to exchange the occupied territories for occupied Ukrainian territory in the event of possible negotiations with Russia.
Zelenskiy did not comment on the situation in the Russian city of Sudzha in the region, from which Ukrainian troops had retreated, according to the Saturday report by the Ukrainian General Staff.
A map published by the Kiev General Staff in the morning showed a withdrawal of Ukrainian troops from the city.
The Russian Defence Ministry had already announced the recapture of Sudzha on Thursday.
According to the Ukrainian military blog Deepstate, Ukraine has lost further villages in the Kursk region.
Zelenskiy said the Russian army was building up forces at the eastern border of Ukraine, indicating that they intend to attack the Ukrainian city of Sumy.
"The build-up of Russian forces indicates that Moscow intends to keep ignoring diplomacy. It is clear that Russia is prolonging the war," he added.
Later, Zelenskiy said the Ukrainian military had successfully deployed the advanced Neptune anti-ship missile.
"It is a new Ukrainian missile, a precise strike. Its range is 1000 kilometres," Zelenskiy wrote on Telegram, without providing further details about the deployment.
Zelenskiy could have been referring to a strike on a Russian refinery in the Black Sea port city of Tuapse on Friday morning, the Ukrainska Pravda media outlet reported, citing its own sources.
Zelenskiy appointed presidential office chief Andrii Yermak as the chief negotiator for potential peace talks, the presidential office in Kiev said on Saturday.
He acknowledged Ukraine's significant diplomatic progress in Jeddah.
Foreign Minister Andrii Sybiha, Defence Minister Rustem Umerov and Yermak's deputy, Pavlo Palisa, are also part of the delegation.
Yermak is considered the most influential person in Ukrainian politics after Zelensky.
The four negotiators already met with US representatives in Saudi Arabia last week, which led to the resumption of US arms deliveries to Ukraine.
Ukraine has agreed to a US proposal of a 30-day ceasefire, provided Moscow complies. Russia, however, opposes an unconditional ceasefire.
The Kremlin also only recognises the US as a partner for a peace agreement, not the Ukrainian leadership or European states.
The last direct Ukrainian-Russian negotiations took place in 2022 shortly after the start of Russia's full-scale invasion, but ended without results.
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