UN nuclear watchdog head Rafael Grossi on Tuesday warned during a visit to Russia's Kursk nuclear plant that its proximity to ongoing fighting was "extremely serious" following Ukraine's unprecedented cross-border offensive.

Grossi said his tour enabled him to "look at the most important parts" of the plant, which is less than 50 kilometres from fighting between Russian and Ukrainian forces.

"A nuclear power plant of this type so close to a point of contact or military front is an extremely serious fact," Grossi said after visiting the plant.

"The fact we have military activity a few kilometres, a few miles away from here, make it an immediate point of attention," he added.

"At the end of the day, again, this may sound common sense and simple: Don't attack a nuclear power plant."

He said he was in "close contact" with Russian authorities and would visit Kyiv next week to talk to Ukrainian President Volodymyr Zelensky, adding it was "important to talk" and "keep dialogue".

He added the Kursk power plant currently was "operating in a very close to normal conditions".

The International Atomic Energy Agency (IAEA) has repeatedly warned of the dangers of fighting around nuclear plants following Russia's full-scale military offensive into Ukraine in February 2022.

In the first days of the conflict, Russian forces seized the Zaporizhzhia nuclear plant in southern Ukraine, and also briefly held the decommissioned Chernobyl plant in the north.

Ukraine launched its surprise incursion into Kursk on August 6 and has said it is making advances, even as Russian forces move deeper into eastern Ukraine.

Russian President Vladimir Putin last week accused Ukraine of trying to attack the Kursk nuclear power plant, with drone fragments found near its spent nuclear fuel storage facility.

"I was informed about the impact of drones, I was shown some of the remnants of those, signs of impact they had," Grossi said on Tuesday.

The plant lies some 60 kilometres from the Russia-Ukraine border, next to the Seym river, and less than 50 kilometres away from Kursk city, the region's capital with a population of around 440,000. (AFP)