There had been no previous claim of responsibility for the bombings, which killed 34 people and heightened security fears before next month's Olympics.
In the video, two Russian-speaking men 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 add that "for the tourists who come there will be a present, too."
The video was posted Sunday on the website of the militant group Vilayat Dagestan.
