The attacks come a day after the former head of an administrative district in Dagestan was killed in the town of Khasavyurt, near the Chechen border.
Russia's mainly Muslim North Caucasus region has experienced a rise in violence in recent months, with Islamist separatist fighters launching attacks on the pro-Kremlin local authorities.
In August, a suicide bombing in Ingushetia killed at least 20 people and wounded more than 70 others in an attack on a police station.
The rising violence throughout the North Caucasus is undermining the Kremlin's claims to be enforcing effective law and order in the region.
While large-scale fighting from the two wars that ravaged Chechnya since 1994 has ended, rebel fighters continue to mount hit-and-run attacks and skirmishes with Russian and Chechen security forces.