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Ukrainian authorities said the safety of the Zaporizhzhia nuclear power plant in Ukraine, Europe's largest, was now secured, after a fire broke out on Friday when the station came under fire from Russian forces.
"The director of the plant said that the nuclear safety is now guaranteed," Oleksandr Starukh, head of the military administration of the Zaporizhzhia region, said on Facebook.
"According to those responsible for the plant, a training building and a laboratory were affected by the fire."
"No country other than Russia has ever fired on nuclear power units," Mr Zelenskyy said in a video message.
"This is the first time in our history. In the history of mankind."
Mr Zelenskyy appealed for global help.
"If there is an explosion, it is the end of everything. The end of Europe. This is the evacuation of Europe. Only immediate European action can stop Russian troops," he said.
The International Atomic Energy Agency said on Twitter that it had been informed by Ukraine’s nuclear regulator that “there has been no change reported in radiation levels” at the nuclear power station.
The agency said its Director General, Rafael Grossi, was in touch with Ukraine’s Prime Minister Denys Shmyhal and the Ukrainian regulator and operator about the situation at the Zaporizhzhia plant.
Mr Grossi “appeals for halt of use of force and warns of severe danger if reactors hit", the IAEA said in another tweet.
An official in Mr Zelenskyy’s office said the reactors had not been damaged and radiation levels were normal.
Andriy Tuz, spokesman for the plant in Enerhodar, earlier said in a video posted on Telegram: “We demand that they stop the heavy weapons fire."
Mr Tuz told Ukrainian TV that shells were falling directly on the Zaporizhzhia plant.
“There is a real threat of nuclear danger in the biggest atomic energy station in Europe,” Mr Tuz said.
The plant accounts for about one quarter of Ukraine’s power generation.
A live-streamed security camera linked from the homepage of the nuclear power plant showed what appeared to be armoured vehicles rolling into the plant's parking lot and shining spotlights on the building where the camera was mounted.
There are what appear to be bright muzzle flashes from vehicles and then nearly simultaneous explosions in the surrounding buildings. Smoke then rises and drifts across the frame.
The Russian military has struck cities in Ukraine with shells and missiles, forcing civilians to hide in basements, including in Chernobyl, the site of the world's worst nuclear disaster.
But Ukrainian Foreign Minister Dmytro Kuleba warned that a disaster at the Zaporizhzhia plant would be far worse.
"Russians must immediately cease the fire, allow firefighters, establish a security zone," Mr Kuleba tweeted earlier.
He said Russian forces were firing at the facility "from all sides".
Mr Tuz, and Enerhodar Mayor Dmytro Orlov, said there was an urgent need to stop the fighting to put out the flames.
US President Joe Biden spoke on Thursday evening with Mr Zelenskyy to receive an update on the fire, the White House said.
Mr Biden joined Mr Zelenskyy "in urging Russia to cease its military activities in the area and allow firefighters and emergency responders to access the site", the White House said.
He also received an update on the situation from the US Energy Department's undersecretary for nuclear security, it said.
At emergency UN Security Council talks on Friday, US ambassador Linda Thomas Greenfield said a nuclear calamity had been averted in southeastern Ukraine by the "grace of God".
The UN’s political chief Rosemary DiCarlo said fighting around nuclear power stations broke international law and was “highly irresponsible”.
Britain’s UN ambassador Barbara Woodward said it was the “first time a state has attacked a fuelled and functioning nuclear power plant”.