The violence in the city of Mukhachevo, near the Polish and Hungarian borders, broke out at a sports facility reportedly controlled by a national parliament member from a faction opposed to Right Sector.
Details remained unclear, but Interior Minister Arsen Avakov said some armed men have been surrounded and are being offered the chance to surrender.
A Right Sector statement reported by Ukrainian news media said two of the militia's members had been killed. Anton Gerashchenko, an adviser to the interior ministry, said three were killed and that three policemen and four civilians were wounded. He also said the attackers destroyed two police cars with grenade launchers.
Right Sector was one of the most militant factions in the massive protests in Ukraine's capital that led to pro-Russia president Viktor Yanukovych fleeing the country in February 2014.
After war broke out in eastern Ukraine between government forces and pro-Russia separatists several months later, Right Sector has fought on the government side and Amnesty International has accused the group of holding civilians as prisoners and torturing them.
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