• International Atomic Energy Agency chief Rafael Grossi said the "plant and physical integrity of the plant" had been "violated several times".
• The inspectors were accompanied to the plant by Russian soldiers after a risky journey delayed by shelling.
UN nuclear experts have made their first inspection of the Russian-held Zaporizhzhia power plant in Ukraine and are to maintain a presence there.
International Atomic Energy Agency chief Rafael Grossi said the "plant and physical integrity of the plant" had been "violated several times".
The inspectors were accompanied to the plant by Russian soldiers after a risky journey delayed by shelling.
Russia and Ukraine accused each other of trying to sabotage the mission.
Zaporizhzhia, in southern Ukraine, is Europe's largest nuclear plant. It was occupied by Russia soon after it invaded Ukraine in February.
Ukrainian staff who continue to operate the plant say Russian troops have used it as a military base and that workers are in effect held at gunpoint.
"We are not going anywhere. The IAEA is now there, it is at the plant and it is not moving - it's going to stay there," Mr Grossi said, once he had crossed back into Ukrainian-held territory.
But he did not specify how many people would be staying and for how long.
Russia's Interfax news agency reported that around eight to 12 inspectors would stay on, while Ukraine's state nuclear company Energoatom said five inspectors would stay.
The inspectors hope to assess the state of the plant and talk to Ukrainian workers under Russian control.
Mr Grossi said that battles taking place near the plant were "not going to stop" the inspection.
"There were moments where fire was obvious, heavy machine gun, artillery mortars, at two or three times [it was] really very concerning, I would say, for all of us," he said.
The IAEA's former chief inspector Olli Heinonen has told the BBC that if interviews do take place, workers are unlikely to be as "open as they would like to be" over the risks to the safety of themselves and their families.
During his nightly address, Ukrainian President Volodymyr Zelensky said he hoped the inspectors would "draw objective conclusions," but lamented the absence of international journalists among the delegation.
"We have clear evidence that Russia did a lot of cynical things to deceive the mission," he added. "The occupiers forced people to lie to the IAEA representatives - to hand over some papers, sign something, say something."
Meanwhile, Mr Zelensky's chief of staff accused Russia of trying to "wreck" the mission by shelling the nearby town of Enerhodar, which is under Moscow's control, and the facility.
"Criminals must be stopped," Andriy Yermak wrote on Telegram, accusing Russia of acting like a "terrorist state".
Russia refuted this, stating that 60 Ukrainian "saboteurs" who attempted to recapture the plant by crossing the river on Thursday morning were killed.
The EU is giving more than five million anti-radiation tablets to Ukraine, as fears grow of an accident at the plant.
While recent fighting in the area has caused some damage to the plant, so far there has not been any recorded increase in radiation levels in the area.