TASS reported that the Russian Interior Ministry database showed Zelenskiy was on a wanted list but gave no further details.
Ukraine's foreign ministry noted Russian President Vladimir Putin was himself subject to arrest under an International Criminal Court warrant.
"We would like to remind you that unlike the worthless Russian announcements, an International Criminal Court warrant for the arrest of Russian dictator Vladimir Putin on suspicion of war crimes is quite real, and subject to implementation in 123 countries," the foreign ministry said in a statement.
It said the Russian announcement was "evidence of the desperation of the Russian state machine and propaganda, which can think of no other way to attract attention".
Ukrainian officials say a Russian attack on Kharkiv injured four civilians. (AP PHOTO)
Russia has issued arrest warrants for a number of Ukrainian and other European politicians since the start of the conflict with Ukraine in February 2022.
Russian police in February put Estonian Prime Minister Kaja Kallas, Lithuania's culture minister and members of the previous Latvian parliament on a wanted list for destroying Soviet-era monuments.
Russia also issued an arrest warrant for the International Criminal Court prosecutor who last year prepared Putin's war crimes warrant.
Meanwhile, there were explosions in both the eastern Ukrainian city of Kharkiv and the western Russian city of Belgorod following a Russian air strike, officials said.
According to regional military administrator Oleh Syniehubov, there were four injured civilians in Kharkiv - three men and one woman, he said on Saturday on Telegram.
Aerial bombs were also dropped on the village of Cherkassky Tyshky near the border, Syniehubov said.
There were also reports of a loud explosion on the opposite side of the border in Russia at about the same time, leading to some media outlets speaking of the possibility of a misdirected Russian bomb.
In Belgorod, the regional governor of the western Russian region, Vyacheslav Gladkov, said: "There was an explosion in Belgorod."
Gladkov said he was on his way to the scene of the accident.
He spoke of five injured, but - in contrast to previous Ukrainian attacks - gave no details of the cause of the detonation.
Pictures show severe damage.
In addition to a destroyed house, where the projectile hit, about 30 neighbouring buildings were also damaged.
The regional independent Telegram channel Pepel wrote: "A Russian aerial bomb probably fell on a house in Belgorod."
In the past, bombs intended for Ukraine have been accidentally released from Russian warplanes too early, causing destruction on Russian soil.
Recently, however, there have been reports that Russia is now increasingly using guided glide bombs that hit their target more accurately, even from a greater distance.
with DPA
