"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 has not preserved its 1991 borders. The signing of the Geneva memorandum on April 17 reaffirmed the willingness of Russia, the United States and EU countries to reach a compromise. While the sides continue to trade tough talk and symbolic sanctions, the Kremlin and the White House are also holding a parallel dialogue on the coordinated geopolitical revision of Eastern Europe.