Speaking at an emergency Cabinet meeting, Prime Minister Arseniy Yatsenyuk said Russia was behind seizures of several government buildings in eastern regions that have for weeks seen a spike in secessionist sentiment.
"The plan is to destabilise the situation, the plan is for foreign troops to cross the border and seize the country's territory, which we will not allow," he said, adding that people engaged in the unrest have distinct Russian accents.
Yatsenyuk said Russian troops remain stationed within 30 kilometres of the frontier.
Police in Luhansk said they have been put on alert and have blocked all entrances to the city.
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A crowd of pro-Russian activists stormed the building yesterday. Local media reported that demonstrators pelted the building with eggs, and then stones, a smoke grenade and finally a firebomb. The flames were reportedly quickly extinguished.
Police said nine people were injured during the assault on the building.
About half of the region's residents are ethnic Russians, many of whom believe Ukraine's acting authorities are Ukrainian nationalists who will oppress Russians.
Ukraine's interim authorities deny they are infringing the rights of the ethnic Russian population. Russia has moved large contingents of troops to areas near the Ukrainian border, and speculation is strong that unrest in eastern Ukraine could be used as a pretext for a Russian incursion.
Since Crimea held a secession referendum and then was annexed by Russia in March, calls for similar votes in Ukraine's east have emerged.