However, they did not elaborate on the fall of the city of Luhansk.
According to the BBC, Russian forces have taken control of the town of Keminna, home to some 18,000 inhabitants, according to earlier reports.
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The British Defense Ministry said Russian forces were engaged in fierce fighting with Ukrainian forces south of the city of Izum as they tried to advance north and south into Sloviansk and Kramatorsk.
Russian forces are believed to be trying to encircle the highly secure Ukrainian positions in the Danbas region, they said. They also said that Ukrainian forces were preparing to defend themselves against the possibility of Russian forces attacking the town of Zaporizhiya from the south.
The BBC has not been able to independently verify the information.
Russia launched a major offensive in the eastern Danbas provinces last week after failing to take control of the Ukrainian capital, Kiev. If they take control of the region, they will be able to connect Moscow-occupied Crimea in 2014 with areas occupied by pro-Russian Ukrainian separatists in the east.
Russia’s Defense Ministry says it has destroyed six Ukrainian railway installations used to supply foreign weapons in the Danbas region.
The head of Ukraine’s state-owned railway company said Russia had fired missiles at five Ukrainian railway stations on Monday, killing one railway worker and wounding four others.