Ukraine has told some residents to leave Kupiansk, as Russia seeks to re-take the city in left last year.
Kharkiv’s military command urged families and those “with limited mobility” to leave due to “constant” shelling by Russian forces.
Russia took the city, an important supply hub, early in the full-scale invasion, with Ukraine re-capturing it last September.
Meanwhile, Wagner group says it troops have “practically encircled” Bakhmut.
Earlier this week, President Zelensky admitted the situation in Bakhmut – around 80 miles south of Kupiansk – was becoming “more and more difficult”.
In Kupiansk, the Kharkiv Regional Military Administration said the evacuation order was due to the “unstable security situation” caused by Russia’s shelling of the town and its surroundings.
It said those evacuated would be provided with assistance, including accommodation, food, humanitarian aid and medical support.
Other citizens are also permitted to leave the region, it added. The city had a pre-war population of around 25,000.
The Institute for the Study of War said this week that Russian forces were continuing “limited ground attacks” north-east of Kupiansk, as well as offensive operations around Kreminna, around 50 miles south.
Kupiansk – home to an important railway junction – has witnessed fierce fighting since the war began, with Russia taking control in a matter of days, and occupying the city for several months.
However, in September Ukrainian forces took back control amid a rapid counter-attack in the country’s east that saw several towns brought under Kyiv’s command.
Those advances were the most significant frontline changes since Russia withdrew from areas around Kyiv in April.
While the evacuation in Kupiansk suggests a worsening situation there, Bakhmut has seen fierce fighting for months.
Yevgeny Prigozhin, head of the paramilitary group Wagner, on Friday said his fighters have “practically encircled” Bakhmut, with only one road remaining. He called on President Zelensky to abandon the city.