Zelenskyy said in his regular evening address, "Any actions by Russia that could trigger the shutdown of the reactors will once again put the station one step away from disaster."
State nuclear company Energoatom said earlier Friday that one of the power plant’s six reactors had been reconnected to the Ukrainian grid. It was disconnected from the electric grid for the first time in its history on Thursday after a fire caused by shelling damaged a power line, Kyiv said.
"The Zaporizhzhia nuclear power station is connected to the grid and is producing electricity for the needs of Ukraine," Energoatom said in a statement.
The plant needs power to run the reactors’ cooling system, and any extended power failure could put the plant in jeopardy of a meltdown.
The power outage at the plant heightened dread of a nuclear disaster in a country still haunted by the 1986 explosion at Chernobyl.
Authorities Friday began providing iodine tablets to residents who live near the nuclear power plant in the event of a radiation leak, as fears grew that the fighting around the plant could spark a catastrophe.
Iodine tablets help block the absorption of radioactive iodine by the thyroid gland, and they were handed out to people in the city of Zaporizhzhia, which is about 45 kilometers from the plant.
Continued shelling was reported around the plant overnight Thursday into Friday, and satellite images from Planet Labs have shown fires burning around the complex over the past several days.
Russia invaded Ukraine in February and took control of the nuclear plant in March, though it is still operated by Ukrainian technicians working for Energoatom.
The nuclear plant remains near the front line and repeatedly has come under fire in recent weeks. Ukraine and Russia have accused each other of shelling the facility.
An engineer working under Russian occupation since March 4 at the nuclear power plant has told VOA that Russian forces have placed artillery and missile installations within and around the property of the plant.
The engineer, whose identity is being withheld for fear of retaliation by the occupying authorities, supports Ukrainian government claims that Russia itself is responsible for the explosions.
Moscow accuses Ukraine of firing on the plant.
Western leaders have demanded that Russia hand the plant back to Ukraine, while U.N. Secretary-General Antonio Guterres has called for it to be "demilitarized."
On Friday, French President Emmanuel Macron warned against the use of civilian nuclear facilities as an instrument of war.
"War in any case must not undermine the nuclear safety of the country, the region, and all of us. Civil nuclear power must be fully protected," Macron said during a visit to Algeria.
Zelenskyy repeated Ukraine's demand Friday that the U.N.’s International Atomic Energy Agency (IAEA) be given immediate access to visit the Zaporizhzhia plant.
A team from the IAEA is expected to send a mission soon to inspect the power station.
On Thursday in Washington, White House press secretary Karine Jean-Pierre told reporters that "Russia should agree to the demilitarized zone around the plant and agree to allow an International Atomic Energy Agency visit as soon as possible to check on the safety and security of the system.”
Meanwhile, Russia's Defense Ministry said Friday that its forces had destroyed a U.S.-made M777 howitzer, which it claimed Ukraine had used to shell the Zaporizhzhia nuclear plant, Reuters reported.
Reuters could not immediately verify the claim.
The Russian Defense Ministry said the howitzer had been destroyed west of the town of Marganets, in Ukraine's Dnipropetrovsk region.
On the battlefield, the General Staff of the Ukrainian Armed Forces said its troops had repulsed Russian assaults on the towns of Bakhmut and Soledar in the eastern Donetsk region, and they also struck ammunition depots and enemy personnel in the southern Kherson region.