The facility, which is Europe’s largest nuclear power plant, is close to the southern front line and has been repeatedly shelled. Both Russia and Ukraine put the blame for shelling the facility at one another’s feet.
Regional governor of the Zaporizhzhia region, Oleksandr Starukh, has now said that civilians close to the plant are receiving instruction on how to use potassium iodide.
A spokesperson added the pills were being handed out for a 50km radius from the power plant.
They added that the measure was undertaken “in case of any future radiation leak”.
Potassium iodide pills offer around 24 hours’ of protection from radioactive iodine absorbed through the thyroid glands.
The mayor of Enerhodar, where the Zaporizhzhia power plant is located, said 25,000 pills had been given to local residents.
Radiation levels are still registering as normal in the surrounding area, despite the shelling.
This comes after Ukraine’s state nuclear energy body, Energoatom, said there was a serious risk of “leakage” at the facility, which has had alarm bells ringing across the globe since the invasion began.
The plant is under Russian control, but is operated by Ukrainian staff.
Mr Zelenksy said on Thursday: “If the diesel generators hadn’t turned on, if the automation and our staff of the plant had not reacted after the blackout, then we would already be forced to overcome the consequences of the radiation accident.”
On Tuesday afternoon, the UN’s nuclear watchdog reported that it had been told by Ukrainian authorities that laboratory and chemical facilities in Zaporizhzhia had been damaged by shelling last weekend.
The former head of the nuclear facility then described the situation at Zaporizhzhia as “very bad now”, and “worsening all the time”.
On Monday, the UN’s International Atomic Energy Agency (IAEA) said a team of inspectors was en-route to Enerhodar after months of petitioning both sides.
Rafael Grossi, who heads up the IAEA, tweeted: “We must protect the safety and security of Ukraine’s and Europe’s biggest nuclear facility.”