Ukraine's state nuclear power company Energoatom blamed Russian shelling for the damage at the Zaporizhzhia power station, Europe's largest.
Earlier, the Russian-installed administration of the occupied Ukrainian city of Enerhodar said Ukrainian shells struck the lines at the plant, in the country's southeast
The Interfax news agency cited the city administration as saying fire had broken out on the plant's premises and that power necessary for the safe functioning of reactors had been cut off.Â
The plant was captured by Russian forces in early March in the opening stage of the war.
Energoatom said the plant - located about 200km northwest of the Russian-held port of Mariupol - still worked and no radioactive discharges had been detected.
Further east, both sides claimed small advances while Russian artillery bombarded towns and villages across a wide area in a now-familiar tactic.
Fighting on the ground appeared to be most intense around Pisky in Donetsk region, a fortified village held by Ukrainian troops and close to Donetsk city, which is in the hands of Russian-backed separatist forces.
The Russian forces also have the cities of Bakhmut and Avdiivka in their sights as they try to gain full control of the eastern Donbas area, Ukraine's industrial heartland.
In other developments, three grain ships left Ukraine's ports on Friday and the first inbound cargo vessel since the Russian invasion was due in Ukraine to load, marking further steps in the Ukrainian government's efforts to resuscitate its economy after five months of war.
Russian President Vladmir Putin meanwhile was meeting Turkish President President Tayyip Erdogan, who is cultivating a role as a mediator in the war, in the Russian city of Sochi.
"The international community cannot end the war in Ukraine by ignoring Russia," Fahrettin Altun, a top aide to Erdogan, said.
Turkey helped negotiate the agreement that on Monday resulted in the first grain ship leaving a Ukrainian port for foreign markets since the Russian invasion on February 24.
On Friday, two grain ships set off from Chornomorsk and one from Odessa carrying a total of about 58,000 tonnes of corn, the Turkish defence ministry said.
The Turkish bulk carrier Osprey S, flying the flag of Liberia, was expected to arrive in Chornomorsk on Friday to load up with grain, the Odessa regional administration said.
Russia and Ukraine normally produce about one third of the world's wheat, and the United Nations had warned that the halt in grain shipments through the Russian-dominated Black Sea could lead to famine in other countries, particularly in Africa, Asia and the Middle East.
"We expect that the security guarantees of our partners from the UN and Turkey will continue to work, and food exports from our ports will become stable and predictable for all market participants," Ukrainian Infrastructure Minister Oleksandr Kubrakov said after the three ships set off on Friday.
Ukrainian Deputy Economy Minister Taras Kachka said he hoped the deal would be extended to other commodities such as iron ore.
Ukraine's Seaport Authority said on Monday 68 ships were berthed in Ukrainian ports with 1.2 million tonnes of cargo on board, two thirds of it food.
Since Russian troops poured over the border in February in what Putin termed a "special military operation," the conflict has settled into a war of attrition fought largely in the east and south of Ukraine.
Russia is trying to gain control of the largely Russian-speaking Donbas, comprised of Luhansk and Donetsk provinces, where pro-Russian separatists seized territory after the Kremlin annexed Crimea to the south in 2014.
Russia's TASS news agency on Friday cited separatist forces as saying they and Russian troops had taken full control of Pisky.
But Ukrainian presidential adviser Oleksiy Arestovych said: "There is very little evidence of any movement here. They (Russian forces) made an attempt to advance but it was unsuccessful."
Ukraine has turned the village into a stronghold, seeing it as a buffer against Russian-backed forces holding Donetsk city about 10km to the southeast.