Ukraine has ordered some residents to leave Kupiansk, as Russia seeks to re-take the city it left last year.
Kharkiv’s regional authorities said families with children and people “with limited mobility” must leave due to “constant” shelling by Russian forces.
Russia seized the north-eastern city early in the full-scale invasion, with Ukraine recapturing it last September.
Meanwhile, Russian mercenaries say they have “practically encircled” the key city of Bakhmut in eastern Ukraine.
The comments were made by Yevgeniy Prigozhin, who heads the paramilitary Wagner group.
In its latest news bulletin, Ukraine’s military said Russian troops continued their offensive on Bakhmut – but the attacks were “repelled”.
Earlier this week, Ukrainian President Volodymyr Zelensky admitted the situation in Bakhmut – about 130km (80 miles) south-east of Kupiansk – was becoming “more and more difficult”.
In Kupiansk, the Kharkiv regional military administration said on Thursday the evacuation order was due to the “unstable security situation” caused by Russian shelling.
It said those evacuated would be provided with assistance, including accommodation, food, humanitarian aid and medical support.
Other citizens were also permitted to leave the region, it added. The city had a pre-war population of around 25,000.
The military said 812 children are currently registered in Kupiansk and the surrounding district, as well as 724 disabled people. (BBC)