It was not clear if the incidents in the southern republics of Chechnya and Ingushetia were coordinated, but Russian officials said they believe one of the region's armed groups was responsible for all the attacks.
The bloodiest attack was in Chechnya, where a suicide car bomber killed three police and wounded four other when a vehicle blew up before dawn outside a police station in the village of Sernovodsk, the Interior Ministry said.
Russian news reports cited local officials as saying the car was speeding toward the station and exploded after police raised a barrier at the station.
In Ingushetia, which borders Chechnya on the west, police spotted a car believed to contain insurgents and began chasing it. The occupants of the car opened fire and then blew up the vehicle, wounding two officers, the ministry said.
Earlier Monday, a man bearing an automatic weapon and wearing a belt of explosives approached a police station in the Ingush town of Ordzhonikidzevskaya, but was intercepted by police and persuaded to surrender, the ministry said.
Islamic rebels have fought two full-scale wars with Russian troops in Chechnya over the past 20 years. Although the insurgency has been largely suppressed, sporadic attacks persist. Ingushetia also suffers frequent violence attributed to insurgents.