In an emotional speech in the middle of the night, Ukraine President Volodymyr Zelenskyy said he feared an explosion that would be "the end for everyone. The end for Europe. The evacuation of Europe."

"Only urgent action by Europe can stop the Russian troops," he said.

"Do not allow the death of Europe from a catastrophe at a nuclear power station."

The assault triggered a phone call between US President Joe Biden and Mr Zelenskyy, and the US Department of Energy activated its nuclear incident response team as a precaution.

The attack on the eastern city of Enerhodar and its Zaporizhzhia nuclear plant unfolded as the invasion entered its second week and another round of talks between the two sides yielded a tentative agreement to set up safe corridors to evacuate citizens and deliver humanitarian aid.

Nuclear plant spokesman Andriy Tuz told Ukrainian television that shells were falling directly on the facility and had set fire to one of its six reactors.

That reactor is under renovation and not operating, but there is nuclear fuel inside, he said.

Firefighters cannot get near the flames because they are being shot at, he said, and Ukrainian Foreign Minister Dmytro Kuleba tweeted a plea to the Russians to stop the assault and allow fire teams inside.

"We demand that they stop the heavy weapons fire," Mr Tuz said in a video statement.

"There is a real threat of nuclear danger in the biggest atomic energy station in Europe."

The assault renewed fears that the invasion could damage one of Ukraine's 15 nuclear reactors and trigger another emergency like the 1986 Chernobyl accident, the world's worst nuclear disaster.

US Energy Secretary Jennifer Granholm tweeted the Zaporizhzhia plant's reactors were protected by robust containment structures and were being safely shut down.

Most experts have seen saw nothing to indicate an impending disaster.

The International Atomic Energy Agency said the fire had not affected essential equipment and that Ukraine's nuclear regulator reported no change in radiation levels.

The American Nuclear Society concurred, saying that the latest radiation levels remained within natural background levels.

"The real threat to Ukrainian lives continues to be the violent invasion and bombing of their country," the group said in a statement.

Jon Wolfsthal, who served during the Obama administration as the senior director for arms control and nonproliferation at the National Security Council, said the plant's reactors have thick concrete containment domes that should protect them from tank and artillery fire.

But he too was concerned about a potential loss of power at the plant, which could imperil its ability to keep the nuclear fuel cool.

The mayor of Enerhodar said earlier that Ukrainian forces were battling Russian troops on the city's outskirts.

Video showed flames and black smoke rising above the city of more than 50,000, with people streaming past wrecked cars, just a day after the UN atomic watchdog agency expressed grave concern that the fighting could cause accidental damage to Ukraine's 15 nuclear reactors.

Prior to the shelling, the Ukrainian state atomic energy company reported that a Russian military column was heading toward the nuclear plant.

Loud shots and rocket fire were heard at the site.

"Many young men in athletic clothes and armed with Kalashnikovs have come into the city. They are breaking down doors and trying to get into the apartments of local residents," the statement from Energoatom said.

Later, a live-streamed security camera linked from the homepage of the Zaporizhzhia plant showed what appeared to be armoured vehicles rolling into the facility's parking lot and shining spotlights on the building where the camera was mounted.

Then there were what appeared to be muzzle flashes from vehicles, followed by nearly simultaneous explosions in surrounding buildings.

Smoke rose into the frame and drifted away.