"We have eliminated a group responsible for the deaths of law-enforcement officers," said Adilgerei Magomedtagirov.
Police had besieged three militants taking shelter in an apartment building late on Monday. One of them attempted to make his escape during the hours of darkness, and was detained by security forces in the street. The other two were killed when the operation resumed on Tuesday morning.
The predominantly Muslim republic of Daghestan borders Chechnya, the violence-stricken republic which has seen two wars with Russia since 1994. Chechen militants are believed to frequently cross into Daghestan, launching attacks on Russian security forces.
On September 30, nine civilians and a senior police official were shot dead by unknown assailants in two separate incidents in the republic.