Six people were killed after two guided bombs hit the DIY hypermarket in a residential area of the city, Regional Governor Oleh Syniehubov said on national television.

At least two of the dead were store employees. Forty people were injured, with at least three in serious condition. Sixteen people were still unaccounted for, Syniehubov said.

Kharkiv Mayor Ihor Terekhov said about 120 people had been in the hardware store when the bombs struck.

"The attack targeted the shopping centre, where there were many people - this is clearly terrorism," Terekhov said.

The past week has seen an uptick in strikes on the city after Russian troops stormed across the border, opening a new front north of the city.

Russia has bombarded Kharkiv, which lies about 30 kilometres (20 miles) from its border, throughout the war, having reached its outskirts in a failed bid to capture it in 2022.

Just over the border, in Russia's Belgorod region, the regional governor said four residents died in Ukrainian attacks on Saturday.

President Volodymyr Zelenskiy issued a plea to Ukraine's Western allies to help boost air defences to keep the country's cities safe. French President Emmanuel Macron, writing on social media platform X, denounced the attack on the store as "unacceptable."

A separate early evening missile strike hit a residential building in the centre of the city of 1.3 million, injuring 18 people, Syniehubov said.

The missile left a crater several metres deep in the pavement at the foot of the building, which also housed a post office, a beauty salon and a cafe.

Emergency workers ushered away residents of nearby apartment buildings. Some of the injured had blood on their faces.

FIREFIGHTERS BATTLE BLAZE

Andriy Kudinov, director of the suburban shopping centre, told local media the hardware store was full of shoppers buying items for their summer cottages.

Huge clouds of dark smoke billowed into the sky over the shopping centre. Firefighters battled many small blazes. Within 90 minutes, most were brought under control.

Rescuers, medics and journalists rushed away from the scene of both strikes and lay on their stomachs, fearing a second strike, as has occurred during several recent Russian attacks.

Witnesses described panicked scenes at the shopping centre.

"I was at my workplace. I heard the first hit and ... with my colleague, we fell to the ground. There was the second hit and we were covered with debris. Then we started to crawl to the higher ground," said Dmytro Syrotenko, 26, who had a large gash on his face.

Syrotenko told Reuters he was taken to safety by a rescue worker who helped him, several colleagues, and shoppers.

Zelenskiy, in his nightly video address, denounced the strike as "yet another example of Russian madness. There is no other way to describe it."

"When we tell world leaders that Ukraine needs sufficient air defences, when we say we need real decisive measures to enable us to protect our people, so that Russian terrorists cannot even approach our border, we are talking about not allowing strikes like this to happen," he said.

Writing later on Telegram, Zelenskiy noted air raid alerts had been in effect in Kharkiv for more than 12 hours and 200 emergency workers and 400 policemen remained at the scene dealing with the aftermath of the attacks.

Moscow denies deliberately targeting civilians, but thousands have been killed and injured during its 27-month invasion of Ukraine.