UN chief Antonio Guterres has called for an end to military activity around Ukraine's Zaporizhzhia nuclear power complex after the plant was hit five more times.
Moscow and Kyiv again blamed each other for the renewed shelling that hit the plant's administrative office and fire station on Thursday.
The UN Security Council met to discuss the situation.
Russia seized Europe's largest nuclear power plant in March after invading Ukraine on February 24.
The plant is still run by its Ukrainian technicians. Ukraine's Energoatom said the area was struck multiple times on Thursday, including near the site where radioactive materials are stored.
Russia's Defence Ministry said in a statement the Ukrainian shelling had partly damaged a thermal power plant and splash pools that form part of the reactors' cooling systems.
Mr Guterres urged the withdrawal of military personnel and equipment and for no more forces or equipment to be deployed.
He called for Russia and Ukraine not to target the facilities or surrounding area.
"The facility must not be used as part of any military operation," Mr Guterres said in a statement.
"Instead, urgent agreement is needed at a technical level on a safe perimeter of demilitarisation to ensure the safety of the area."
Ukraine's President Volodymyr Zelenskyy accused Russia of using the nuclear power plant "to threaten the entire world".
"Only a full withdrawal of the Russians from the territory of the Zaporizhzhia nuclear power station and the restoration of full Ukrainian control of the situation around the station can guarantee a resumption of nuclear security for all of Europe," Mr Zelenskyy said in his nightly video address.
'The brink of nuclear catastrophe'
IAEA chief Rafael Grossi briefed the 15-member Security Council on Thursday at the request of Russia.
Mr Grossi said that he was ready to lead an IAEA mission to Zaporizhzhia and called on Russia and Ukraine to cooperate so inspectors could travel as soon as possible.
"The IAEA has been ready to perform such a mission since June when we were ready to go. But unfortunately, due to political factors and other considerations, it was not possible," Mr Grossi told the council, adding that all military action around the plant needed to stop.
Russia's UN ambassador Vassily Nebenzia said the trip agreed between Russia and the IAEA in June was cancelled by UN security officials.
"We believe it justified for IAEA representatives to go to the Zaporizhzhia nuclear power plant as quickly as possible and possibly even before the end of August," Mr Nebenzia told the Security Council.
He said the world was being pushed "to the brink of nuclear catastrophe, comparable in scale with Chernobyl".
UN spokesman Stephane Dujarric has said the UN was committed to doing everything possible to get the IAEA technicians to Zaporizhzhia.
"There's a war going on, and we're talking about a nuclear power plant in the middle of a battlefield," Mr Dujarric told reporters on Thursday.
"I think we can think of at least two or three pages' worth of hurdles."
Zelenskyy tells officials to stop talking about Ukraine's tactics
The Ukrainian President on Thursday told government officials to stop talking to reporters about Kyiv's military tactics against Russia, saying such remarks were "frankly irresponsible".
In the wake of major blasts that wrecked a Russian air base in Crimea on Tuesday, the New York Times and Washington Post newspapers cited unidentified officials as saying Ukrainian forces were responsible.
The government in Kyiv, on the other hand, declined to say whether it had been behind the explosions.
"War is definitely not the time for vanity and loud statements. The fewer details you divulge about our defence plans, the better it will be for the implementation of those defence plans," Mr Zelenskyy said in an evening address.
"If you want to generate loud headlines, that's one thing — it's frankly irresponsible. If you want victory for Ukraine, that is another thing, and you should be aware of your responsibility for every word you say about our state's plans for defence or counter attacks."
Mr Zelenskyy addressed his remarks to state, local and military officials as well as other people he said were commenting on events at the front.
Pictures released by independent satellite firm Planet Labs showed three near-identical craters where buildings at the air base had been struck. The burnt-out husks of at least eight destroyed warplanes were clearly visible.
ABC/wires
