On Thursday, Russian forces took control of more territory to the south of Severodonetsk and Lysychansk, raising fears that Ukrainian forces could soon be encircled there.
Image: BBC
Ukrainian forces in Severodonetsk have been ordered to withdraw, according to the top regional official.
The city is the focus of Russia's invasion as it tries to take control of large parts of eastern Ukraine.
"Remaining in positions that have been relentlessly shelled for months just doesn't make sense," Luhansk regional head Serhiy Haidai said.
Russian forces have nearly encircled Severodonetsk in recent days, and are now targeting its twin city Lysychansk.
"They have received orders to retreat to new positions... and from there continue their operations," Mr Haidai told Ukrainian television on Friday morning.
The city's entire infrastructure has been completely destroyed, he added, with over 90% of houses shelled and 80% of them critically damaged.
It is unclear if the Ukrainian withdrawal has begun - Ukrainian military said on Friday morning that "fighting continues for the city of Severodonetsk".
On Thursday, Russian forces took control of more territory to the south of Severodonetsk and Lysychansk, raising fears that Ukrainian forces could soon be encircled there.
Russia's invasion of Ukraine, which began on 24 February, has been focused on the two cities for several weeks.
They are the last significant Ukrainian positions in the Luhansk region, which together with the Donetsk region make up what is collectively known as Donbas.
Russian President Vladimir Putin has falsely claimed that Russian speakers in the Donbas have for years been the victims of genocide - one of the key justifications he uses for invading Ukraine.
Ukraine dismisses Mr Putin's claim as baseless, and accuses Moscow of committing genocide against the Ukrainian people.
In a separate development on Friday, a Russian-appointed official in the occupied southern city of Kherson was killed in a car blast, Russian news agencies reported.
Ukraine, whose forces have made advances in the area, has made no public comment on the issue.
Several Kremlin-installed officials have recently been targeted in the Kherson region, control over which allows Moscow to have a land corridor from Russia to Crimea - Ukraine's southern peninsula annexed by the Kremlin in 2014.