Officials in Dagestan, on Chechnya's eastern border, said police and troops had surrounded a house overnight after observation suggested it was a centre for extremist activity.
The occupants refused to surrender and, after children were allowed to leave, a gunbattle erupted, lasting until after dawn. Four men were killed and three women were taken into custody in the regional capital, Makhachkala.
Meanwhile, in Ingushetia, to the west of Chechnya, Interfax news agency said that rebels had opened fire with machine guns on a car carrying Russian servicemen, killing three of them. The agency, quoting prosecutors, said a number of soldiers had been injured.
Upsurge in violence
Alu Alkhanov, Chechnya's pro-Moscow president acknowledged that separatist rebels still posed a problem in the region despite the killing last month of the most prominent guerrilla, Shamil Basayev.
"Basayev's removal makes our fight against armed fighters easier, but does not solve the problem entirely"
Alu Alkhanov, Chechnya's pro-Moscow president
Restating Russian allegations that separatists secure funding from radical groups abroad, Alkhanov said: "We realise that we are dealing with a powerful network of international terrorism, including Al-Qaeda,
"Basayev's removal makes our fight against armed fighters easier, but does not solve the problem entirely."
Nikolai Patrushev, head of the FSB counter-intelligence agency, told the same gathering on Friday that Islamist separatists intended to hit targets in nearby regions.
"Terrorists have shifted the accent of their activities to the territory of the republics bordering Chechnya," he said.
Despite recurring attacks on its forces there, Moscow says the region is under control and functioning normally under a pro-Moscow government.