Secretary-General Antonio Guterres has issued a call for forces "to cease immediately" all military activity near the power plant, the largest of its kind in Europe, "and not to target its facilities or surroundings."
"Urgent agreement is needed at a technical level on a safe perimeter of demilitarization to ensure the safety of the area," Guterres said.
"Regrettably, instead of de-escalation, over the past several days there have been reports of further deeply worrying incidents that could, if they continue, lead to disaster," he added.
Bombing continued on Wednesday night along the front line in Ukraine, including near the plant in the southeast of the country occupied by Russian troops.
Russia's occupation of the plant has alarmed the international community, with the G7 group of most industrialized nations warning on Wednesday that it "endangers the region," and calling for return of the facility to Ukrainian control.
Guterres echoed the warning, saying "potential damage to Zaporizhzhia or any other nuclear facilities in Ukraine, or anywhere else, could lead to catastrophic consequences not only for the immediate vicinity, but for the region and beyond."
The secretary-general's statement comes ahead of a UN Security Council emergency meeting called by Russia for Thursday afternoon to address the crisis at the complex.
The UN nuclear safety watchdog, the International Atomic Energy Agency, said its Director General Rafael Grossi would brief the Security Council meeting "about the nuclear safety and security situation" at the plant as well as his "efforts to agree and lead an IAEA expert mission to the site as soon as possible."
The United States supports calls by the United Nations and others to establish a demilitarized zone around the Zaporizhzhia nuclear plant in Ukraine, now occupied by Russian forces, the State Department said Thursday.
"We continue to call on Russia to cease all military operations at or near Ukrainian nuclear facilities and return full control to Ukraine, and support Ukrainian calls for a demilitarized zone around the nuclear power plant," said a State Department spokesperson.
Ukraine and Russia have been at war since Moscow invaded its neighbor in late February and their forces have clashed at and around Zaporizhzhia.