"A gunfight started in which four police were killed and six injured," an official with the regional police force said. He said casualties among the fighters were unknown.
"The gunfight has been under way four about five hours now."
Three other police officers travelling with the dead policeman were also injured when their car came under fire.
Located on the Caspian Sea coast, the republic of Dagestan is part of the Russian Federation and is one of several restive regions in the Russian Caucasus.
A weekend clash in Ingushetia was officially said to have left three soldiers dead, although some news reports said the real toll was far higher.
Both Dagestan and Ingushetia border Chechnya, the scene of two full-scale wars since the collapse of the Soviet Union in 1991.
Federal forces have largely pacified Chechnya, but attacks have increased in the neighbouring regions in recent months.
Human rights organisations have said that unemployment, a lack of opportunities and tough reprisals by security bodies have pushed young men in Dagestan towards movements fighting against the Moscow government.