A pro-Russian spokesperson confirmed the fighting and even said Ukrainian troops had entered the town itself, though this remained unconfirmed.
There were also unconfirmed claims that a second helicopter had been forced to make an emergency landing after being attacked, with its pilot being taken hostage.
Recent weeks have seen insurgents seizing police stations and other government buildings in about a dozen cities in southeastern Ukraine.
Similar incidents occurred in Crimea before Vladimir Putin annexed the Ukrainian region.
The EU and US have hit Russian individuals with sanctions and threatened further measures if Mr Putin does not act to de-esculate the crisis.