Kupjansk is a vital hub for the railway in the Kharkiv region. The city has been subjected to deadly artillery fire from Russian forces just a few kilometers away over the past few months.
The region's governor, Oleh Sinehubov, warned earlier in the week that the authorities can no longer guarantee electricity and water to the residents due to the attacks.
"In total, around 10,000 people need to be evacuated. The evacuation rate is increasing every day," he says on Friday in a video published on Telegram.
Before the war, almost 30,000 people lived in Kupjansk.
Ukraine announced on Friday that it has received the bodies of 501 soldiers who fell in battles against Russian forces, mainly in eastern Ukraine.
"As a result of repatriation efforts, 501 bodies of fallen Ukrainian defenders have been returned to Ukraine," says an organization dealing with prisoner-of-war issues in a statement.