The death toll from a Russian strike on a hardware superstore in the eastern Ukrainian city of Kharkiv rose to 11 Sunday, the regional governor said, with President Volodymyr Zelensky condemning the attack as "vile".

"Unfortunately, the death toll at 'Epitsentr' has increased to 11 people," Kharkiv regional governor Oleg Synegubov said on Telegram, referring to the store hit on Saturday.

Earlier, he said six people had "died on the spot", 40 were wounded and 16 were missing after two guided Russian bombs hit the store.

Two of those killed "were men who worked in the hypermarket", Synegubov said in a video on Telegram.

Thick black smoke billowed from the gutted Epitsentr superstore on the northeastern outskirts of the city, as firefighters sprayed water on a blaze sparked by the strikes, AFP journalists saw.

The Epitsentr chain sells household and DIY goods.

Still wearing her uniform, Lyubov, a cleaner at the store, recalled how she escaped the building.

"It happened all of a sudden. We didn't understand at first, everything went dark and everything started falling on our heads," she said.

"It was good that my phone lit up, thanks to the flashlight I found where to go, but in front of us everything was burning already."

- 'Obviously civilian' target -

"As of now, we know that more than 200 people could have been inside the hypermarket," Zelensky said Saturday on Telegram, condemning the daylight attack on an "obviously civilian" target.

French President Emmanuel Macron wrote on X that Russia's strikes on the store were "unacceptable".

"France shares the pain of the Ukrainians and remains fully mobilised alongside them," he said.

Russia's TASS state news agency cited a security source claiming that a missile strike destroyed a "military store and command post" inside the shopping centre.

The regional governor said there was "no contact with some of the staff" and "according to our information, visitors could still be in the building".

Kharkiv, Ukraine's second-largest city, is just a few dozen kilometres from the border and regularly comes under attack from Russian missiles.

Synegubov said the city was under "massive rocket fire all day" on Saturday.

- 'Brutal blow' -

Later Saturday, another strike hit the centre of Kharkiv, wounding 14 in an area containing a post office, a hairdresser and a cafe, the city's mayor Igor Terekhov said.

Zelensky had visited Kharkiv on Friday and met with officials to discuss the defence of the surrounding region.

On Saturday, he urged world leaders to supply Ukraine with "sufficient air defence protection" to "prevent such terrorist attacks".

"Russia struck another brutal blow at our Kharkiv -- at a construction hypermarket -- on Saturday, right in the middle of the day," Zelensky said.

"Only madmen like Putin are capable of killing and terrorising people in such a vile way," he said, referring to the Russian president who ordered his troops into Ukraine in February 2022.

The latest attacks came after Russia launched a ground offensive in the Kharkiv region on May 10. Ukraine said Friday that it had managed to halt Moscow's progress and was counterattacking.

Ukraine's rescue service posted images of firefighters spraying water inside the blazing Epitsentr store building, with the roof torn open and debris strewn around.

They said the fire had raged over an area of 10,000 square metres (108,000 square feet) but that the firefighters had managed to contain it.

"There were a lot of workers and shoppers inside," Zelensky said.

He said later that the hypermarket had "burned to the ground" and that nearly 60 people had been wounded in Kharkiv throughout the day.

- Border strikes -

Russia and Ukraine accused each other's forces of attacks along the border Saturday.

Russia said Ukraine shelled a small town in the Belgorod region, killing two people and wounding 10.

Ukraine said Russia shelled the village of Kupiansk-Vuzlovyi, a railway hub in the region of Kharkiv, wounding five, the regional prosecutor's office said.

It said two vehicles came under fire: a car with two passengers and an ambulance with a driver, a paramedic and a 64-year-old patient.

Russia also carried out air strikes on the Kupiansk district, damaging a factory and residential buildings, prosecutors said.

In the eastern Donetsk region, shelling on Saturday killed a 40-year-old woman and wounded four other people, said the head of the regional administration, Vadym Filashkin.