"Servicemen of the Russian Defense and Interior Ministries engaged eight armed militants belonging to an illegal armed group active in the Shatoi district," a police source said.
He said no servicemen were injured in the operation, and the bodies were being identified.
On Friday, an Mi-8 transport helicopter crashed in the area, killing 20 troops and crew. Russian military in the troubled republic said it had been shot down my small arms fire. But Chechen authorities cited a mechanical fault as the cause of the crash.
It was the second-deadliest crash of a federal helicopter in Chechnya in recent years, after the downing of a heavy Mi-26 Halo helicopter August 19, 2002, which killed 127 on board.
Fighting in the troubled republic has largely died down in recent years, following two bloody separatist wars, but occasional clashes between local police, federal troops and armed groups still erupt.
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Ukraine will not be a unitary state following the developments of last winter, spring and summer, says a report by the Valdai Club experts, which has been distributed on the sidelines of the 11th annual meeting of the Valdai International Discussion Club that is underway in Sochi.