Back-up diesel generators ensured power supply that is vital for cooling and safety systems at the plant, Zelenskiy said, praising the Ukrainian technicians who operate the plant under the gaze of the Russian military.
Residents in the capital Kyiv, some 556 km (345 miles) to the northwest of the plant, expressed alarm at the situation.
Russia's Defence Ministry said on Friday its forces had destroyed a U.S.-made M777 howitzer which it said Ukraine had used to shell the Zaporizhzhia plant.
Russia invaded Ukraine in February, captured the plant in March and has controlled it since, though Ukrainian technicians still operate it.
Russia and Ukraine have accused each other of shelling the site, fuelling fears of a nuclear disaster.
1/5 Overview of Zaporizhzhia nuclear power plant and fires, in Enerhodar in Zaporizhzhia region, Ukraine, August 24, 2022.
Nuclear experts have warned of the risk of damage to the plant's spent nuclear fuel pools or its reactors. »