STORY: The plant was captured by Russian forces in March during the early stages of its invasion of Ukraine but is still run by Ukrainian technicians.
On Wednesday Ukrainian authorities performed disaster response drills following repeated shelling at the plant, the largest of its kind in Europe.
Both sides accuse the other of attacks in the vicinity of the facility in recent days and engaging in what they call "nuclear terrorism."
In his nightly address, Zelenskiy said Ukrainian diplomats, nuclear specialists, and the International Atomic Energy Agency (IAEA) are working to send an IAEA mission to Zaporizhzhia.
Moscow calls its invasion an operation to demilitarise its neighbor and protect Russian-speaking communities. Ukraine and its allies accuse Russia of waging an imperial-style war of conquest.