The nuclear power plant in south-eastern Ukraine is Europe’s largest, and was captured by Russian forces back in March. The facility is still operated by Ukrainian staff, with Ukrainian officials claiming they are obligated to carry out orders under threat of torture.
The plant, close to the front line and the town of Enerhodar, has come under heavy shelling in recent weeks.
Moscow blames Kyiv for the shelling, whereas Ukrainian authorities insist Russia is responsible for the attacks.
The International Atomic Energy Agency (IAEA) has repeatedly called for independent inspection of the facility and an immediate stop to shelling in close proximity to the nuclear plant.
On Tuesday afternoon, the IAEA reported that it had been told by Ukrainian authorities that laboratory and chemical facilities in Zaporizhzhia had been damaged by shelling over the weekend.
The organisation said transformers at a nearby thermal power plant had sustained damage, which had disrupted a power line linking the two facilities on Monday.
The connection was then restored after several hours.
On Monday, the former head of the nuclear facility described the situation at Zaporizhzhia as “very bad now”, and “worsening all the time”.
Petro Kotin told Sky News: “Over the last three weeks, there’s been an increase of shelling at the site.
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He added that Ukrainian staff were being pushed to “accept the Russian world”, and that contact was frequent but extremely limited.
Russia’s defence ministry has previously said it may shut down the nuclear power plant, should shelling continue.
The head of Russia’s radioactive, chemical and biological defence forces said the radioactive fallout of an accident at Zaporizhzhia could have wide-reaching impacts across Europe.
He pinpointed Germany, Poland and Slovakia as most in the firing line.
Rafael Grossi, who heads up the IAEA, has said he would “plead” with both sides to allow independent inspection of the plant.
He called the facility “out of control”, before saying on Tuesday that a mission could access the site within days if an agreement is reached.
Mr Grossi said: “The mission is expected to take place within the next few days if ongoing negotiations succeed.”