One police officer was killed and three others wounded when their patrol in the Daghestani town of Khasavyurt was attacked late on August 25.
The police officers were investigating a tip that a suspect was nearby when they approached a bridge in the town and came under fire.
Police and security forces are reportedly searching for the attackers.
The security situation in Daghestan and other Russian republics in the North Caucasus has been deteriorating in recent months.
Attacks on members of law-enforcement agencies and local officials have been increasing in Daghestan, Ingushetia, and Kabardino-Balkaria.
Eight policemen were killed by a suicide bomber on August 18 in Ingushetia as they attended a funeral for a slain comrade.
Based on reporting by ITAR-TASS and Interfax