The head of the key eastern city of Severodonetsk says the front line has cut the city in half.
But Oleksandr Stryuk says Ukraine is holding out and still defending its positions there.
The area's regional governor says the situation is grave after Russians entered the city.
The entire region is under continuous bombardment, Serhiy Haidai says.
Moscow now occupies almost all of the Luhansk region, which it recognised as independent before the invasion in February.
European Union leaders are holding a second day of talks, having agreed on a plan to cut Russian oil imports yesterday.
Russia has stopped supplying gas to the Netherlands after Dutch energy firm GasTerra refused to pay in roubles.
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