Two suspected Islamist militants and a police officer were killed in Ingushetia, while a blown-up car with three bodies was found in Dagestan, Interfax said.
Three assailants fired machines guns at the unidentified police officer in Nazran on Friday before fleeing, it said.
The suspected militants, Ilez Dauberkov and Aliskhan Kuzigov, were killed in a skirmish with police officers who stopped their car for a document check. Two other occupants of the car escaped and fled into a wood, Interfax said, citing the Federal Security Service.
The burned-out car with three bodies was found near the village of Gurbuki in Dagestan late Saturday, a police spokesman told Interfax. It remained unclear who the victims were.