The fire that broke out at Ukraine's Zaporizhzhia power plant due to Russian firing has been extinguished, said a post on Ukrainian State Emergency Service's Facebook page.

“At 06:20 [09:20am PST] the fire in the training building of Zaporizhzhia NPP in Energodar was extinguished. There are no victims,” the statement said.

Earlier fire broke out in a training building at the largest nuclear power plant in Europe during intense fighting between Russian and Ukrainian forces, Ukraine's state emergency service said on Friday.

US Energy Secretary Jennifer Granholm said there was no indication of elevated radiation levels at the Zaporizhzhia plant, which provides more than a fifth of total electricity generated in Ukraine.

A video feed from the plant verified by Reuters showed shelling and smoke rising near a building at the plant compound.

The footage shot at night showed one building aflame, and a volley of incoming shells, before a large candescent ball lit up the sky, exploding beside a car park and sending smoke billowing across the compound.

The mayor of the nearby town of Energodar about 550 km (342 miles) southeast of Kyiv said fierce fighting and "continuous enemy shelling" had caused casualties in the area, without providing details.

Thousands of people are believed to have been killed or wounded and more than 1 million refugees have fled Ukraine since Russian President Vladimir Putin last Thursday launched the biggest attack on a European state since World War Two.

Early reports of the incident at the power plant sent financial markets in Asia spiralling, with stocks tumbling and oil prices surging further.

"Markets are worried about nuclear fallout. The risk is that there is a miscalculation or over-reaction and the war prolongs," said Vasu Menon, executive director of investment strategy at OCBC Bank.

Russia has already captured the defunct Chernobyl plant, about 100 km north of Kyiv, which spewed radioactive waste over much of Europe when it melted down in 1986. The Zaporizhzhia plant is a different and safer type, some analysts said.

U.S. President Joe Biden spoke with Ukrainian leader Volodymyr Zelenskiy to get an update on the situation at the plant.

"President Biden joined President Zelenskiy in urging Russia to cease its military activities in the area and allow firefighters and emergency responders to access the site," the White House said.

Energy Secretary Granholm said on Twitter the reactors at Zaporizhzhia were "protected by robust containment structures" and were being "safely shut down".

The International Atomic Energy Agency said in a tweet that it was "aware of reports of shelling" at the power plant and was in contact with Ukrainian authorities.