In the south, 73 Russian soldiers were killed and 13 pieces of equipment and ammunition depots were destroyed as Ukrainian forces sought to take control of new territory, the regional command said on Facebook.
"In the course of the ensuing battle, (our) units fired on the enemy, which, as a result, was obliged to return to its original position with losses of tanks, armoured vehicles and personnel."
Reuters could not immediately verify the battlefield accounts.
FEARS OF NUCLEAR CATASTROPHE
Russia says its aim in Ukraine is to demilitarise the country and protect Russian-speakers on land that President Vladimir Putin says historically belongs to Russia.
Ukraine and the West call it an unprovoked war of conquest. Ukraine shook off Russian domination when the Soviet Union broke up in 1991.
Guterres reiterated calls for demilitarisation around the nuclear plant.
"The facility must not be used as part of any military operation. Instead, agreement is urgently needed to re-establish Zaporizhzhia's purely civilian infrastructure and to ensure the safety of the area," Guterres said.
Russia, which captured the plant in southern Ukraine soon after the Feb. 24 invasion, said it could shut it down, which Ukraine warned would increase the risk of a nuclear catastrophe.
Russia had earlier rejected as "unacceptable" international calls for a demilitarised zone. Ukrainian engineers are still operating the plant despite the Russian occupation.
The power station sits on the Russian-controlled south bank of a huge reservoir in Enerhodar; Ukrainian forces hold the north bank. Russia and Ukraine traded accusations through the night of shelling civilian areas near the power station, as they have done for days.
Ukraine also accuses Russia of using the plant as a shield for its forces to launch strikes across the reservoir on Ukrainian-held cities, which Russia denies.
Reuters cannot independently confirm the military situation in the area or the responsibility for shelling.
Zelenskiy said after meeting Guterres that they had agreed parameters for a possible mission to the plant by the UN nuclear watchdog, the International Atomic Energy Agency.
"Russia should immediately and unconditionally withdraw its forces from the territory of Zaporizhzhia nuclear power plant, as well as stopping any provocations and shelling," Zelenskiy said.