"We don't know how severe their injuries are," the source said, adding that a search for the militants is underway.
The clash occurred near the village of Gudben in the republic's Karabudakhkent district.
Security forces have linked the incident to the ingoing investigation into the murder of Nurmagomed Gadzhimagomedov, a 59 year-old priest at a local mosque. Gadzhimagomedov was shot on September 29 on his way to morning prayer, a day after he had spoken out against Islamic extremists during a service.
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.
