The militants were killed on the Kavkaz highway between the settlements of Baksan and Islamei on Monday.
"The militants have been identified. They are residents of the republic. Gang leader Adam Shigalugov has been on the international wanted list," NAK said. "They were involved in a number of crimes, such as attempted murders of police, murders of civilians and extortion of large sums of money from business people.
The operations headquarters in the Kabardino-Balkar republic said it has imposed the regime of anti-terrorist operation in the Zolsky district.
"The regime has been effective on an area that includes the villages of Shardakovo, Svedlovskoye, Zolskoye and Zalukodes," an official at the headquarters told ITAR-TASS. It envisions special measures and temporary restrictions.