Four were shot dead in a rural region of predominantly Muslim Dagestan, the National Anti-Terrorism Committee said.
“(The men) opened fire with automatic weapons on law enforcement officials and as a result of the firefight the militants were fatally wounded,” the agency said in a statement.
Three others were killed in separate firefights in two other regions of Dagestan. An eighth suspected rebel was killed in the nearby North Caucasus region of Kabardino-Balkaria.
Russian security forces are trying to staunch an insurgency in the North Caucasus, between the Caspian and the Black Sea, where militants want to establish an Islamist state. Dagestan, on the Caspian Sea, is the epicentre of the insurgency.
Deadly violence in the North Caucasus, which has its roots in two separatist wars in Russia’s Chechnya and is a near daily occurrence, is a particular focus for Moscow as it is not far from Sochi where Russia plans to hold the 2014 Winter Olympics.
US investigators are looking into possible ties between Tamerlan and Dzhokhar Tsarnaev, ethnic Chechens who are accused of carrying out the Boston bombings and who lived briefly in Dagestan, and militants in the North Caucasus.