A video posted Sunday on the website of the militant group Vilayat Dagestan appeared to show two Russian-speaking men warning about upcoming suicide attacks and threatening tourists who will be visiting the Olympics site.
The men also claimed responsibility for the twin bombings at a train station and on a bus in the city of Volgograd last December that killed 34 people.
In the video, the pair were seen sitting in front of black banners with Arabic verses warn President Vladimir Putin that if the games are held, "we will give you a present for the innocent Muslim blood being spilled all around the world."
They added that "for the tourists who come there will be a present, too."
There had been no previous claim of responsibility for the bombings.
The 50-minute-long video appeared to show people holding rifles and preparing explosives. There was also a security footage of the twin bombings.
It is unclear when the video was filmed. The two men in the video have not been identified.
The video comes one day before the Olympic torch relay is scheduled to pass Volgograd.