Russia has said the leader of a North Caucasus al-Qaeda linked armed group has been killed in an operation by special forces, with the rebels confirming his death.

Russia's National Anti-Terrorism Committee said on Monday that Aliaskhab Kebekov, also known as Ali Abu Mukhammad, was "neutralised" during an operation in Dagestan.

Kebekov took over the leadership of the Caucasus Emirate last year after the death of its founder, Doku Umarov, who had claimed responsibility for major attacks in Russia.

The 43-year-old had pledged allegiance to al-Qaeda and last month was added to a US government list of global "terrorists".

Founded in 2007, the Caucasus Emirate is a loose alliance of rebel groups seeking to create an independent Islamic state in the North Caucasus, a predominantly Muslim region that includes Chechnya and Dagestan.

The Kavkaz Centre website, which is used by rebels to release statements, confirmed Kebekov's death, saying that "our dear brother became a martyr".

Volgograd bombings

Forces from Russia's FSB security force and interior ministry surrounded the rebels in a building and opened answering fire after attempts to negotiate broke down, the committee said.

The building where the rebels were hiding was destroyed during the fighting and the bodies were pulled out from under the collapsed walls, the Russian authorities said.

Those in the building included women, who refused to leave, while a child was handed out and survived, the committee said.

Russia said four others were killed, including two regional leaders of the group, during the operation in the town of Buinaksk, which began on Sunday and ended on Monday.

Moscow said Kebekov was directly involved in organising suicide bombings in the southern city of Volgograd in 2013 that killed 34 people.

It said he also played a crucial role in the financial structure of the Caucasus Emirate "practically organising the extortion of money from the public".

Kebekov was declared wanted by Russia in 2012.