Five separatist rebels and three policemen have been killed in a gunbattle in Russia's unstable Caucasus region, authorities said Tuesday.

The clash on the border between the provinces of Karachayeva-Cherkessia and Stavropol in the western part of the Caucasus follows Monday's suicide bombing in the eastern Dagestan province that killed one soldier and wounded six others.

Two regional police officials confirmed Tuesday's clash. They spoke on condition of anonymity because they were not authorized to speak publicly on the matter. One or two rebels fled into the nearby forest and police are hunting for them, one official said.

Violence attributed to separatists seeking an Islamic state in the Caucasus is less frequent in Karachayeva-Cherkessia than in the other Caucasus provinces of Dagestan, Ingushetia and Chechnya, where police and suspected insurgents are killed almost daily.

Rights activists say authorities fuel the bloodshed, which stems from two separatist wars in Chechnya, with brutal crackdowns on civilians.

In Chechnya's capital, Grozny, police acting on a tip killed two suspected suicide bombers who had refused to surrender on Tuesday, according to Magomed Deniyev, a police spokesman for the province. Explosives and detonators were found on the would-be bombers, Deniyev said.