Kyiv warned of a Chornobyl-style catastrophe and appealed for the area to be a demilitarised zone over shelling attacks on Ukraine's Zaporizhzhia nuclear complex.
The UN chiefs called for UN nuclear inspectors to be given access to the plant, as Kyiv and Moscow blamed each other for the shelling.
UN Secretary General Antonio Guterres said on Monday that any attack on a nuclear plant is a suicide.
Petro Kotin, head of Ukraine's state nuclear power company Energoatom, called for a team of peacekeepers to be deployed at the Zaporizhzhia site, which is still run by Ukrainian technicians.
The decision that we need from the world community and all our partners is to withdraw the invaders from the territory of the station and create a demilitarised zone on the territory of the station, Mr Kotin said on television.
Russia has accused Russia of trying to cause electricity blackouts in government controlled areas of Ukraine's south, according to the International Atomic Energy Agency, Ukraine's ambassador to the UN nuclear watchdog agency, Yevhenii Tsymbaliuk.
He called for a UN-led mission to the plant by the end of the month.
As soon as possible, we really need it, said Mr Tsymbaliuk.
The RIA Novosti news agency quoted Moscow's ambassador to the IAEA who said Russia was ready to facilitate a visit to the reactor complex.
The worst civil nuclear disaster occurred in 1986 when a reactor at the Chornobyl complex in northwest Ukraine exploded.
Mr Guterres said IAEA personnel needed access to the Zaporizhzhia to create conditions for stabilisation. Ukraine said it is planning to conduct a major counter-offensive in the Russian-occupied south, focusing on the city of Kherson, west of Zaporizhzhia, and that it has already taken over dozens of villages.
A deal to unblock Ukraine's food exports and ease global shortages gathered pace as two grain ships sailed out of Ukrainian Black Sea ports on Monday, raising the total to 12 since the first vessel left a week ago.
The two newest outgoing ships were carrying almost 59,000 tons of corn and soybeans and were bound for Italy and southeastern Turkey.
The four left that were left on Sunday bore almost 170,000 tons of corn and other food.
The July 22 grain export pact brokered by Turkey and the United Nations is a rare diplomatic triumph as fighting churns on in Ukraine and aims to help alleviate soaring global food prices arising from the war.
Russia and Ukraine accounted for nearly a third of global wheat exports before the invasion.
Since then, the disruption has raised the spectre of famine in parts of the world.
Ukraine hopes to export 20 million tons of grain in silos and 40 million from its new harvest to help rebuild its economy.
Russian forces are trying to gain full control of Ukraine's eastern Donbas region, where pro-Moscow separatists seized territory after the Kremlin annexed Crimea to the south in 2014.
Ukrainian soldiers are firmly holding the defence, inflicting losses on the enemy and ready for any changes in the operational situation, Ukraine's General Staff said on Monday.
Russian forces stepped up attacks north and northwest of Russian-held Donetsk city in the Donbas on Sunday, Ukraine's military said.
It said Russians pounded Ukrainian positions near the heavily fortified settlements of Piski and Avdiivka, as well as shelling other locations in the Donetsk province.