Shellfire at the Russian-occupied Zaporizhzhia nuclear power plant in Ukraine fuelled fears of a major disaster as both sides kept blaming the other, while Russian forces targeted towns on the far side of the river from Europe's largest atomic plant.

Despite the danger, officials from the United Nations nuclear watchdog were still waiting for clearance to visit the plant on the southern front line of the war.

Standing beside a crater at a school that had been largely reduced to rubble, the governor of the Zaporizhzhia region, Oleksandr Starukh, told Ukrainian television that people were being informed how to apply iodine in case of a radiation leak.

He was speaking in the city of Zaporizhzhia, two hours drive from the plant, which sits along the vast Kakhovka reservoir on the Dnipro river.

Russian forces seized the plant in early March soon after invading Ukraine, while Ukrainian staff continue to operate it. In recent weeks both countries have traded blame for shelling near the plant.

Ukraine's state nuclear company Energoatom said Russian troops again shelled the grounds of the complex in the last 24 hours. "The damage is currently being ascertained," Energoatom wrote in a statement on Telegram.

Moscow's defense ministry on Saturday accused Ukrainian forces of shelling the plant complex three times in 24 hours. It said in a statement that 17 shells were fired, with four hitting the roof of a building storing "168 assemblies of U.S. Westinghouse nuclear fuel."

It said 10 shells exploded near a dry storage facility for spent nuclear fuel and three near a building that houses fresh nuclear fuel storage. It said the radiation situation at the plant remained normal.

Reuters could not verify either side's report.

Ukraine's President Volodymyr Zelenskyy said earlier Friday the situation at Zaporizhzhia remained "very risky" after two of its six reactors were reconnected to the grid following shelling that caused the nuclear plant to be disconnected for the first time.

The head of the International Atomic Energy Agency (IAEA), Rafael Grossi, said Thursday the U.N. agency was "very, very close" to being able to send officials to inspect the plant.

Energoatom's statement on Saturday said its staff at the plant had come under "increased pressure" ahead of the likely visit, "to hush up their testimonies about the crimes of the occupiers at the station and using it as a military base."

U.N. Secretary-General Antonio Guterres called this month for military equipment and personnel to be withdrawn from the plant to ensure it is not a target.

On the opposite shore from the Zaporizhzhia plant, the towns of Nikopol and Marhanets were hit by shells on Saturday afternoon and evening, Nikopol Mayor Yevhen Yevtushenko said on Telegram.

Fighting rages on

Further south, Russian forces were trying to withstand a Ukrainian counteroffensive centerd around Kherson, the first sizable city to be captured after the invasion was launched six months ago.

Ukrainian strategy has focussed on destroying four bridges Russian forces must hold to supply Kherson, at the southern end of the Dnipro.

Vladimir Leontyev, the Russian-appointed head of the Kherson region, told Russia's TASS news agency that Ukrainian forces had again shelled the Kakhovsky bridge over a hydropower dam.

Ukraine's southern command on Sunday claimed successful artillery and missile attacks in the area, which it said killed 35 Russians and destroyed a howitzer, a self-propelled artillery gun and nine armored and other vehicles.

"Also destroyed were two ammunition depots and one field supply point," it said.

Donbass front

On Ukraine's eastern front, defenders continued to foil Russian attempts to break through around the strategic city of Bakhmut to extend control over the Donbas region.

Having taken Sievierodonetsk and Lysychansk weeks ago, Russian forces have focused on Bakhmut. The town, which had been home to 80,000 people before the war, was shelled again Saturday, as were nearby Soldedar and Zaitsevo, according to a Ukrainian military report.

It said Ukraine halted advances near two other major towns, Sloviansk and Kramatorsk.

The Ukrainian military also said its forces holding out in the coal-producing town of Avdiivka had managed to repel a Russian assault despite enemy artillery and airstrikes.

The Russian defense ministry said in a daily briefing it had destroyed a large ammunition depot in Ukraine's Dnipropetrovsk region that had contained U.S.-made HIMARS rocket systems and shells for M777 Howitzers.

The Russian Air Force shot down a MiG-29 aircraft in the Donetsk region in Donbas, the ministry said, and destroyed six missile and artillery weapons depots in the Donetsk, Mykolaiv and Kherson regions.

Reuters could not verify those accounts.

President Vladimir Putin launched the invasion of Russia's neighbor on Feb. 24, saying a "special operation" was needed to demilitarise the country and remove perceived security threats to Russia.

Ukraine and the West have dismissed this as a baseless pretext for an imperialist war of conquest.