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.
Russia's president 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 its indiscriminate bombing and shelling.
Meanwhile, Russia has said the decision by EU leaders to accept Ukraine and Moldova as membership candidates will have negative consequences.
Russian foreign ministry spokeswoman Maria Zakharova said the EU was sacrificing its democratic ideals at the expense of "unrestrained expansion and the political and economic enslavement of its neighbours".
Most buildings heavily damaged
Severodonetsk has been the target of intense Russian shelling for several weeks and more recently has seen fierce street battles, with Ukrainian forces gradually pushed back to the city's industrial zones.
All bridges to the city have been destroyed by Russian troops as they attempt to cut it off from Ukrainian-held territory. Ukraine's withdrawal may be a last-ditch effort to avoid being surrounded on all sides.
"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 continue their operations from there."
The city's entire infrastructure has been completely destroyed, he added, with over 90 percent of houses shelled and 80 percent of them critically damaged.
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.
Hundreds of civilians are thought to remain in Severodonetsk, many seeking shelter in the sprawling Azot chemical plant. Before the war, the city had a population of around 100,000 people.
Russian forces have made advances in the areas around Severodonetsk and Lysychansk in recent days, with Ukraine's defence ministry describing the settlements to the south and southeast of the cities as the "hottest sector of the front".
But Haidai said it would be "very difficult" for the Russians to seize Lysychansk because the city, which is on a hill, had "many defensive positions".
Aid can still be delivered to the city and civilians are still being evacuated, he said.
Ukrainian forces around the towns of Zolote and Hirske are already completely surrounded, according to Russia's defence ministry.
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 not commented 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 which Russia annexed in 2014.
- BBC