The video was posted on a Chechen extremist site, ABC News reported, considered a credible source for militants in the North Caucasus. Two men were depicted in street clothes before the a black jihad flag cradling assault rifleds.
"We'll have a surprise package for you" if Russia does not withdraw from the Caucasus region, one of the men said, "and those tourists that will come to you, for them, too, we have a surprise. If it happens [the Olympics], we'll have a surprise for you. This is for all the Muslim blood that is shed every day around the world, be it in Afghanistan, Somalia, Syria, all around the world. This will be our revenge," ABC reported.
The video also claimed responsibility for two bombings last month in the Russian city of Volgograd, CNN reported.
Volgograd is a major transit hub about 400 miles away from Sochi. The bombings hit a train station and a trolley bus, killing more than 30 people.
The 2014 Winter Games begin Feb. 6.