One officer was killed and another injured, when unknown gunmen opened fire with automatic weapons at a traffic police vehicle.
The attack occurred near the town of Khasavyurt, west of the republic's capital Makhachkala, late on Monday, when the police vehicle stopped at a food store and one of the officers went to buy food. Two unknown men approached the vehicle from opposite sides and opened fire.
"Two traffic officers were seriously wounded and taken to hospital in Khasavyurt," police said adding that one of them had later died in hospital without regaining consciousness, the other is in a stable condition following an operation.
Daghestan and other Russian republics in the North Caucasus have been unstable following two wars in Chechnya since 1994, with violence spilling over into neighboring regions.
In a separate incident, two police officers died when an unidentified explosive device went off in a wooded area in Chechnya's Kurchaloi district, 30 kilometers (18 miles) east of capital Grozny, during a search operation, a police source said.