Three died in Ingushetia. The Ingush Interior Ministry said they were members of a group that had entered Ingushetia from the wartorn neighboring republic of Chechnya after a battle with police there. Security forces finally cornered them in the border village of Nesterovskaya.
A police officer also died and four others were wounded in the gun battle.
In Daghestan, police shot and killed two alleged militants in the town of Buinaksk. A bystander was injured in the shooting and later died in hospital.
Ingushetia, Daghestan, and other parts of Russia's North Caucasus region have seen a surge in violence over the past year, for which the authorities often blame Chechen rebels.
(compiled from agency reports)