The death toll from a Russian strike on a hardware superstore in the eastern Ukrainian city of Kharkiv rose to 12 Sunday, the interior minister said, with President Volodymyr Zelensky condemning the attack as "vile".

Igor Klymenko, Ukrainian interior minister, said that the fire in the Epitsentr superstore had spread over 13,000 square metres and injured 43 people. Another 16 are still missing, he said Sunday.

"It took more than 16 hours to extinguish a fire in a Kharkiv construction hypermarket caused by targeted Russian strikes," he said on Telegram. "Russian shelling killed 12 people and injured 43 others".

Forensics experts and investigators were still working to identify bodies in the ruins of the Epitsentr DIY store in the northeastern outskirts of the city, Klymenko said.

Earlier, the Kharkiv regional governor Oleg Synegubov said two of the people who had been killed worked in the hypermarket, adding that the city had been under "massive rocket fire all day".

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."

Zelensky condemned the daylight attack on an "obviously civilian" target.

"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.

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

- Peace summit call -

On Sunday, Zelensky urged US President Joe Biden and Chinese leader Xi Jinping to personally attend a planned peace summit in June in Switzerland in a video message showing him in front of the ruins of a publishing house bombed in Kharkiv last week.

"I am appealing to the leaders of the world... to President Biden, the leader of the United States, and to President Xi, the leader of China... Please support the peace summit with your personal leadership and participation," Zelensky said.

The high-level conference on the Ukraine war is to be hosted in Lucerne June 15-16 by the Swiss government, which has said it has invited 160 delegations but Russia will not attend.

Biden has not confirmed his attendance and it is not known if China will attend.

Beijing has said that it supports an international peace conference recognised by both Russia and Ukraine.

For Russia, "it is a pleasure to burn," Zelensky said in his message, describing its bombardment of Kharkiv with S-300 missiles and guided aerial bombs.

Ukraine's air force said that overnight into Sunday Russia launched another 14 missiles and more than 30 attack drones on Ukraine.

It said it downed all but two of the missiles.

In the central Vinnytsia region, fragments from a downed drone wounded three people and damaged houses and blocks of flats, regional authorities said.

On Saturday evening, another strike hit the centre of Kharkiv city, wounding 25 in an area containing multi-storey buildings and a research institute, Synegubov said.

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

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.