Mr Guterres added that any damage to the plant would be “suicide”. He made the comments during a summit with Ukrainian President Volodymyr Zelensky and Turkish President Recep Tayyip Erdogan in the western Ukrainian city of Lviv.
The meeting was the first between Mr Guterres and Mr Zelensky since the start of the Russian invasion in February.
Mr Erdogan echoed the UN chief’s comments telling reporters that he was concerned about “another Chernobyl” disaster occurring at the Zaporizhzhia plant.
Russia seized the area around the plant in March and in recent weeks there has been heavy artillery fire close to the plant.
Kyiv and Moscow have blamed each other for the attacks.
Ahead of the meeting Mr Zelensky slammed “deliberate” Russian attacks on the plant.
Russia has been accused of turning the plant into a military base.
All three leaders urged Moscow to demilitarise the area as soon as possible.
It comes as Ukrainian staff, who are working at the facility under the direction of Russian forces, have warned of a potential nuclear catastrophe.
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Ukraine ‘s centre for information security tweeted that Moscow was preparing for a “provocation” and a “terrorist attack” at the plant.
They said: “Ukrainian intelligence officers believe that the Russians are preparing a provocation at the [facility].
“Following their extensive shelling… [Russian forces] could ‘raise the stakes’ and stage a real terrorist attack on Europe’s largest nuclear facility.”
Mr Zelensky also used the social media channel to warn “the world is on a verge of nuclear disaster” as well as blasting “Russia’s irresponsible actions and nuclear blackmailing”.
However, the Zaporizhzhia plant is said to be much more secure that the Chernobyl plant north of Kyiv, the site of the worst nuclear accident in history in April when Ukraine was a constituent republic of the Soviet Union.
Speaking to the BBC in March experts claimed that the reactor is in a steel-reinforced concrete building that can “withstand extreme external events.”