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 center of the Islamic insurgency that has spread throughout the region following separatist wars in neighboring Chechnya.
In response to the terrorist threat, Russia has introduced sweeping security measures for the Sochi Games.
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Chechen leader of the Caucasus Emirate, Doku Umarov, had ordered a halt to attacks on civilian targets in 2012, but he rescinded that order in July and urged his followers to try to undermine the Olympics.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 couldn't 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.
