An Islamic militant group in Russia's North Caucasus has claimed responsibility for twin suicide bombings in the southern city of Volgograd last month and posted a video threatening to strike the 2014 winter Olympics in Sochi.

There had been no previous claim of responsibility for the bombings, which killed 34 people and heightened security fears before next month's Games.

In the video, two Russian-speaking men warned President Vladimir Putin: "If you hold these Olympics, we will give you a present for the innocent Muslim blood being spilled all around the world: in Afghanistan, in Somalia, in Syria."

They said: "For the tourists who come, there will be a present, too."

In a statement posted with the video on its website, the militant group Vilayat Dagestan claimed responsibility for the Volgograd bombings.

The video claims that the two men, identified as Suleiman and Abdurakhman, were the suicide bombers and purports to show the explosives being prepared and strapped to their bodies.

There was no immediate reaction to the video from the Russian security services.

During much of the 49-minute video, the two men speak to the camera while holding Kalashnikov automatic rifles. Behind them hang black banners with Arabic religious phrases similar to those used by al-Qaida.

Vilayat Dagestan is one of the groups that make up the so-called Caucasus Emirate, which seeks to establish an independent Islamic state in the North Caucasus, a region just to the east of Sochi on Russia's southern border.

Dagestan, one of several predominantly Muslim republics in the North Caucasus, has become the centre of the Islamic insurgency that has spread throughout the region following separatist wars in neighboring Chechnya.

The Chechen leader of the Caucasus Emirate, Doku Umarov, had ordered a halt to attacks on civilian targets in 2012, but he rescinded that order in July and urged his followers to try to undermine the Olympics.

The Kremlin-backed leader of Chechnya claimed last week that Umarov was dead, but the claim could not be verified.

The Vilayat Dagestan statement said the Volgograd attacks were carried out in part because of Umarov's order, but didn't specifically say he had ordered them.