Russia and Ukraine earlier accused each other of trying to sabotage the mission of the International Atomic Energy Agency (IAEA) to the plant in southern central Ukraine, which is controlled by Russian forces but operated by Ukrainian staff.
Conditions at the nuclear plant, Europe's largest, have been unravelling for weeks, with Moscow and Kyiv regularly trading blame for shelling in the vicinity and fuelling fears of a Chernobyl-style radiation disaster.
A Reuters reporter saw the IAEA team arrive in a large convoy with a heavy presence of Russian soldiers nearby.
Ukraine's state nuclear company Energoatom said Russian shelling had forced the shutdown of one of only two operating reactors at the site, while Moscow said it had thwarted a Ukrainian attempt to seize the plant.
A Reuters reporter in the nearby Russian-controlled town of Enerhodar said a residential building was struck by shelling, forcing people to take cover in a basement.
The Russian-installed governor of Zaporizhzhia district, Yevgeny Balitsky, said at least three people had been killed and five wounded in what he said was Ukrainian shelling of Enerhodar that had also destroyed three kindergartens and the House of Culture.
Russia's Foreign Minister Sergei Lavrov said Moscow was doing everything to ensure that the plant could operate safely, and for the IAEA inspectors to be able to complete their tasks.
IAEA chief Rafael Grossi told reporters early on Thursday in the city of Zaporizhzhia, 55km from the plant, he was aware of "increased military activity in the area" but would press ahead with the plan to visit the facility and meet staff.
The IAEA inspectors, wearing body armour and travelling in white, armoured land cruisers with UN markings on their sides, had been held at the first checkpoint outside the city following the shelling reports.
Russia accused Ukrainian forces of trying to seize the plant and also of shelling both the meeting point of the IAEA delegation and the nuclear plant itself.
Russia's defence ministry said up to 60 Ukrainian troops had crossed the Dnipro river, which divides territory held by the two sides, in boats at 6am on Thursday, in what it said was a "provocation" aimed at disrupting the IAEA visit.
The ministry said "measures had been taken" to destroy the opposing troops, including use of military aviation.
A local Russian-installed official, Vladimir Rogov, later said "around 40" of the 60 Ukrainian troops had been killed. Russian troops also captured three Ukrainian servicemen during the assault on the plant, he added.
Ukrainian officials have welcomed the IAEA visit, expressing hope that it will lead to the demilitarisation of the plant.
They have also accused Russian forces of shelling the plant, which Russian officials deny.
Russian-installed officials have suggested that the team from the UN nuclear watchdog would have only a day to inspect the plant, while the mission had prepared for longer.
Both sides have claimed battlefield successes amid a new Ukrainian push to recapture territory in the south.
"It is a very slow process, because we value people," said Oleksiy Arestovych, an adviser to President Volodymyr Zelenskiy, referring to the Ukrainian offensive.
Moscow has denied reports of Ukrainian progress and said its troops had routed Ukrainian forces.
Russia captured large tracts of southern Ukraine close to the Black Sea coast soon after launching its invasion on February 24, including in the Kherson region, north of the Russian-annexed Crimean Peninsula.
In eastern Ukraine, Ukrainian forces repelled Russian attacks in the direction of Bakhmut and Avdiivka, towns north of the Russian-occupied city of Donetsk in Ukraine's industrial Donbas region, Kyiv's military general staff said.
Russian-backed separatists said on Thursday 13 emergency service personnel were killed and nine wounded after coming under Ukrainian artillery fire in the Russian-controlled part of the Donetsk region.
15°C