Each side blamed the other for the shelling on Sunday, and both sides reported that one civilian had been killed.
Russian authorities said "the nationalists of Ukraine" had hit the area, while the Ukrainian mayor of the city, Dmytro Orlov, spoke of a "murderous provocation" by the Russian side.
There was no independent confirmation of the incident.
Europe's largest nuclear power plant, which has been occupied by Russian troops since March, has been subject to shelling for several weeks.
Experts from the International Atomic Energy Agency are due to inspect the site. However, the United Nations, Russia and Ukraine cannot agree on the planning for the visit.
Russian diplomat Mikhail Ulyanov has called on the United Nations to intervene to ensure the safety of the plant.
According to reports, the UN has so far not allowed IAEA chief Rafael Grossi to travel, not only for security reasons, but also because of a dispute over the itinerary.
Grossi could travel under Russian protection via the Black Sea peninsula of Crimea, which was annexed by Moscow in 2014, but this would be perceived as an affront by Kiev.
Ukraine accuses Russian troops of using the nuclear power plant as a fortress from which to fire on the small towns of Nikopol and Marhanez, which lie on the other bank of the Dnipro reservoir.
Russia, on the other hand, claims that Ukraine is shelling the plant with drones, heavy artillery and rocket launchers.
The Kremlin said meanwhile it had hit targets in dozens of places in eastern Ukraine with missiles and artillery.
The attacks were concentrated in the Donetsk region, the Russian Defence Ministry said. In the neighbouring Kharkiv region the village of Udy was captured, Moscow said, and a fuel depot near Sloviansk was destroyed.
The Ukrainian general staff in Kiev reported intense attacks in the east and south of the country. In the Donetsk region, an attempt by Russian forces to break through to Sloviansk had been repelled, it said.
Overall, Kiev said the situation was largely unchanged.
