"The number of dead has grown to 14," Oleg Synegubov, Kharkiv regional governor, said on Telegram, as nearly 200 rescuers worked at the scene.
Interior minister Igor Klymenko said earlier that 43 were injured and "16 people are considered missing", after Russian strikes hit the Epitsentr superstore on Saturday, sparking a massive fire.
"It took more than 16 hours to extinguish the fire in the Kharkiv construction hypermarket caused by targeted Russian strikes," the minister said on Telegram.
Forensics experts and investigators were still working to identify bodies in the ruined store in the northeastern outskirts of the city, Klymenko said.
Earlier, 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 at Ukraine's request.
Bern has said it has invited 160 delegations but that Russia will not attend.
Russian President Vladimir Putin said earlier this month "they are not inviting us".
China has said it supports an international peace conference that is 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.
Russia on Sunday claimed the capture of the village of Berestove in the Kharkiv region, located on the eastern front line close to the Lugansk region.