Ukrainian forces have been ordered to withdraw from Severodonetsk, according to the top regional official.
The eastern city has endured weeks of bombardment, as Russian forces try to take complete control of the region.
A Ukrainian retreat would be significant because it would leave all of Luhansk under Russian control, except for the city of Lysychansk.
Luhansk, a mainly Russian-speaking region in east Ukraine, is a key priority for President Vladimir Putin.
Together with the Donetsk region it makes up what is collectively known as the Donbas – a large, industrial area which has been the focus of a Russian-backed separatist movement since 2014.
Vladimir Putin falsely claims that Russian speakers in the Donbas have been victims of genocide – a key justification for his invasion of Ukraine.
In turn, Ukraine accuses Moscow of committing genocide against the Ukrainian people with the indiscriminate bombing and shelling.Most buildings heavily damaged
Russian forces have nearly encircled Severodonetsk in recent days, and are also targeting its twin city Lysychansk.
“Remaining in positions that have been relentlessly shelled for months just doesn’t make sense,” Luhansk regional head Serhiy Haidai told Ukrainian television.
“They [Ukrainian forces] have received orders to retreat to new positions… and from there continue their operations.”
Severodonetsk district head Roman Vlasenko said Ukrainian troops were still in the city, telling Radio Liberty on Friday that a withdrawal could still take some time.
The city’s entire infrastructure has been completely destroyed, he added, with over 90% of houses shelled and 80% of them critically damaged.
Hundreds of civilians are thought to remain in Severodonetsk, many seeking shelter in the sprawling Azot chemical plant. Before the war, it had a population of around 100,000 people.
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.
But Mr Haidai said it would be “very difficult” for the Russians to seize Lysychansk straightaway because the city, which is on a hill, had “many defensive positions”.
He said civilians were still being evacuated from Lysychansk, and aid was still being delivered to the city, despite roads and bridges leading into the city being destroyed.
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 Russia annexed in 2014.