Security experts say the Russians are right in taking the threat seriously.
The video was posted online Sunday by a militant group in Dagestan, a predominantly Muslim republic in Russia's volatile North Caucasus. The Olympic host city of Sochi lies only 500 kilometers (300 miles) west of Dagestan.
Two Russian-speaking men featured in the video are identified as members of Ansar al-Sunna, the name of a Jihadist group operating in Iraq. It was unclear whether the men in the video had received funding or training from that group or only adopted its name.
There was no confirmation the two men were the suicide bombers who struck the southern Russian city of Volgograd last month as the video claims. Scores of people were also injured by the bombings of a train station and a bus.
Russia's National Anti-Terrorism Committee said Monday it was studying the video and would have no immediate comment. The video couldn't be viewed in Russia, where Internet providers cut access to it under a law that bans the "dissemination of extremist materials."
In Washington, a Pentagon spokesman Monday said the U.S. has offered support to the Russian government as it conducts security preparations for the Winter Olympics. Rear Adm. John Kirby said the U.S. will offer air and naval support, including two Navy ships in the Black Sea, to be available if requested "for all manner of contingencies," in consultation with the Russian government.
The video was released by the Vilayat Dagestan, one of the units that make up the so-called Caucasus Emirate, an umbrella group for the rebels seeking to establish an independent Islamic state in the North Caucasus.
Doku Umarov, a Chechen warlord who leads the Emirate, had ordered a halt to attacks on civilian targets in 2012. But he rescinded that order in July, urging his followers to strike the Sochi Olympics, which he denounced as "satanic dances on the bones of our ancestors." The games run from Feb. 7-23.
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 it didn't specifically say he had ordered them.
Dagestan has become the center of an Islamic insurgency that has engulfed Russia's North Caucasus after two separatist wars in Chechnya. Militants seeking to create an independent state governed by Islamic Shariah law in the Caucasus launch daily attacks on police and other authorities there. One of the two ethnic Chechen brothers accused of staging the Boston Marathon bombings spent six months in Dagestan in 2012.
Andrei Soldatov, an independent Moscow-based security analyst, said the video threat need to be taken seriously.
"They have capabilities to strike beyond the North Caucasus, which they demonstrated in Volgograd," he said. "It's extremely difficult to stop a 'lone wolf' suicide bombing attack."
Georgy Mirsky, a respected Russian expert on the Middle East, said the video reflected the increasingly close ties between Jihadists in the Caucasus and elsewhere. Russia's war against Caucasus militants has made it an enemy on par with the United States and Israel for militant Islamic groups in the Middle East, he wrote on his blog.
Russia has responded to the Islamic threat by introducing some of the most sweeping security measures ever seen at an international sports event. Some 100,000 police, army and other security forces have been deployed, according to analysts, and tight restrictions have been placed on access to the Sochi area.
Anyone attending the Winter Olympics has to buy a ticket online from the organizers and obtain a spectator pass that requires providing passport details.
Authorities have already barred access to all cars registered outside of Sochi and Russian police have gone house-to-house methodically screening all city residents.
Soldatov argued, however, that Russia's massive security presence at the Olympics could also have an adverse effect.
"When you put so many troops on the ground, you might get some problems with the coordination of all these people," he said.
Soldatov noted that the ominous threat of a "present" for the visitors to the Games contained in the video is loosely phrased and could herald an attack outside tightly guarded Olympic facilities.
"They never tried to specify the place where they might strike, that's why everybody should be concerned," he said.
Associated Press writer Lynn Berry contributed to this report.