Ukraine on Monday evening confirmed that Kreminna had fallen to Russian forces.
Russian strikes on Monday killed at least eight civilians in the embattled eastern Ukrainian regions of Donetsk and Lugansk, local authorities said.
Four died as they tried to escape the city of Kreminna which Russian forces captured earlier on Monday, Lugansk regional governor Sergiy Gaiday said on Telegram.
"Several people tried to flee and the orcs (Russian forces) shot the car. Four people died instantly," he said, adding that another person was injured.
Four other civilians died in Russian bombing in the neighbouring region of Donetsk around 20 kilometres (12 miles) east of Kreminna, according to regional governor Pavlo Kyrylenko.
"Two in Torske, one in Chandrigalove and one in Razdolne. Five other people were injured," he said on Telegram.
Russia has refocused its military efforts on Ukraine's eastern Donbas region after withdrawing troops from the region around the capital Kyiv.
Ukraine's security and defence council secretary Oleksiy Danilov confirmed the Russian offensive in the east on Monday.
"Almost along the entire front line in the territory of Donetsk, Lugansk and Kharkiv regions, the invaders tried to break through our defences," he said.
"Fortunately, our military is holding on."
Gaiday on Monday evening confirmed that Kreminna had fallen to Russian forces.
In Ukraine's second city Kharkiv, three people died and 15 were injured after Russian shelling, according to regional governor Oleg Sinegubov.
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