Clashes killed eight rebel fighters in Russia's turbulent North Caucasus, news agencies quoted Chechen President Ramzan Kadyrov as saying, while a police officer died in a separate incident.

"Eight fighters were killed in the past 24 hours" during a "special operation" on the border between Ingushetia and Chechnya, Kadyrov told Interfax news agency.

He said one of those killed was Azamat Makhaury, "who called himself the emir of Ingushetia".

"Ingush and Chechen security forces exchanged fire with a group of militants in mountains in the Sunja region, which borders Chechnya," a police source told RIA Novosti agency earlier.

Azamat Makhaury is the brother of Rustam Makhaury, the defence minister of the separatist Chechen government in exile who was arrested several days ago.

Separately in Dagestan, an insurgency-hit region which like Ingushetia is predominantly Muslim, a senior police officer died after gunmen opened fire on his car, a police source told RIA Novosti.

"The incident took place in the village of Kirov-Aul. Two gunmen armed with assault rifles shot at a car which contained the village police chief," the source said.

Clashes between government forces and Islamist rebels are common in Dagestan and Ingushetia.