Twelve militants and seven Russian policemen have died in a clash in the southern Stavropol region, Russian security officials say.
Russian special forces were deployed to flush out the rebels
The fighting erupted on Thursday in Tukui-Mekteb, a village just north of Chechnya in the North Caucasus.
According to Russian media reports, the militants had seized two houses.
Hostilities flared up again in Chechnya in 1999 and Russia has refused to negotiate with the separatist rebels who want independence.
On Friday up to 300 police officers and elite troops surrounded and then stormed a house in the village where the rebels were holed up, Russian security officials said.
Earlier, several policemen had died in a clash with the rebels.
Villagers were evacuated when the fighting erupted on Thursday.
Russian officials say the rebels belonged to a militant group called Shelkovskoy Jamaat, named after an area in northern Chechnya.
According to a local police chief, the heavily-armed militants had planned to seize a school. Some of them are reported to have escaped.
Security forces have sealed off the village and are searching the area.
Chechnya's infrastructure was devastated by years of intense fighting and the republic still sees sporadic clashes between Russian security forces and separatist rebels.
The violence has spilled over to neighbouring Russian regions, including Dagestan, Ingushetia and North Ossetia.