Severodonetsk has been the centre of the Russia-Ukraine conflict in recent weeks.
Ukrainian troops may have to retreat from the eastern city of Severodonetsk which is being shelled by Russian troops "24 hours a day", the regional governor said on Wednesday.
"It is possible that we will have to retreat" to better fortified positions, Lugansk governor Sergiy Gaiday said in an interview on the TV channel 1+1.
"No one is going to surrender Severodonetsk even if our forces have to fall back to better fortified positions," Gaiday added.
The strategically important city is the focus of Russia's offensive after their forces were repelled from other parts of Ukraine following the February invasion.
Its capture would allow Russia troops to push deeper into the eastern Donbas region and Ukraine's de facto administrative centre there, Kramatorsk.
Gaiday said that fierce fighting was ongoing in Severodonetsk, an industrial city with a pre-war population of around 100,000 people.
"Our forces are fighting for every inch of the city," he said.
The Ukrainian presidency said in a briefing Wednesday morning that two civilians had been killed and two more injured in the broader Lugansk region.
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