Volodymyr Zelenskyy says the world narrowly avoided a catastrophe at the Zaporizhzhia facility, after shelling by Moscow's forces.
Russia has blamed Ukraine's forces for triggering a nearby fire, which led to the reactors shutting down.
The United Nations is seeking access to the power plant and has called for the area to be demilitarised.
"For the first time ever the Zaporizhzhia plant's emergency protection system was activated after Russian shelling damaged the power grid and diesel generators kicked in. The world must understand the threat because if the safeguards had not worked, we'd have a radiation emergency."
