A Russian strike on a supermarket in the eastern Ukrainian town of Kostyantynivka on Friday killed at least 10 people and injured 35, Ukraine's interior minister said.

The town is about 13 kilometres (eight miles) from the nearest Russian positions and faces almost daily strikes.

"10 were killed and 35 others were wounded," Interior Minister Igor Klymenko said in a post on Telegram.

He published photos of firefighters working amid the smouldering rubble of the destroyed building.

AFP journalists saw dozens of people fleeing as police officers warned of a potential second strike.

Plumes of black smoke rose from the building and police cordoned off nearby streets. Drones and an uptick in artillery fire in the area were also audible.

President Volodymyr Zelensky vowed retribution for the attack, which happened in the middle of the day and comes on the fourth day of a major Ukrainian cross-border incursion into Russia's western Kursk region.

"Russia will be held accountable for this terror," he said in a post on Telegram.

Vadym Filashkin, Ukraine's governor of the Donetsk region, said Russian forces had shelled the town with cannon artillery.

"This is another targeted attack on a crowded place," he said.

The strike comes one day after two civilians were killed in the same town, Filashkin reported.