Chechnya: Round two? Battle for the Caucasus Cat-and-mouse conflict Islamic roots in Dagestan Russia's demoralised army

A news agency, which supports the rebels, confirmed the attacks on rebel positions.

Heavy fighting is reported to be continuing around the village of Chabanmakhi, near the border with Chechnya.

Russian commander General Vyacheslav Ovchinnikov said the operation against the rebels would be finished by Friday.

He said his forces had also captured the nearby village of Karamakhi, and surrounded the estimated 120 remaining militants.

The announcements follow unconfirmed reports that Russian troops had already gained control of the two villages by Monday.

Renewed offensive

Russian paratroopers arrest a suspected militant

The new Russian offensive began on Sunday, about 80km (50 miles) to the east of where Russian forces routed rebel fighters last month.

The insurgents, many of whom are said to be members of the fundamentalist Wahhabi sect, had declared an independent Islamic state in the area and seized several villages before being driven out by the Russians.

But the Russians' first push against the rebels stayed away from the Karamakhi region, which is where the Islamists are strongest.