Ukraine has told some residents to leave Kupiansk, as Russia seeks to re-take the city it 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 north-eastern city, an important supply hub, early in the full-scale invasion, with Ukraine re-capturing it last September.
Meanwhile, Wagner group says its troops have "practically encircled" Bakhmut.
Earlier this week, President Volodymyr Zelensky admitted the situation in Bakhmut - around 130km (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 military said 812 children are currently registered in Kupiansk and the surrounding district, as well as 724 disabled people.
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 80km (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 front-line changes since Russia withdrew from areas around Kyiv in April.
Last month Ukraine warned that Russia was preparing a major new offensive, with officials saying Moscow has amassed thousands of troops on Ukraine's eastern flank.
And Defence Minister Oleksii Reznikov warned a month ago that Russia could "try something" to mark the anniversary of the full-scale invasion on 24 February.
But that apparent escalation has not translated into major successes on the battlefield, despite apparent advances around Kupiansk and Bakhmut.
In a video posted on Telegram, Yevgeny Prigozhin, head of the paramilitary group Wagner, on Friday said that "pincers are closing in" around Bakhmut.
In a direct message to President Zelensky, he said Wagner units had "practically encircled" the city, with only one road remaining.
He called on the Ukrainian president to abandon the city.