In a video posted on a well-known jihadi forum, two men believed to have been the suicide bombers in last month's deadly bombings in Volgograd speak of them - and warned of more.
"We've prepared a present for you and all tourists who'll come over," the video says in part.
"If you hold the Olympics, you'll get a present from us for the Muslim blood that's been spilled."
The US-based SITE Monitoring Service on Sunday identified the men as "purported Volgograd bombers Suleiman and Abdul Rahman".
December suicide bombings at a railway station and on a trolleybus in the southern Russian city - which investigators have linked to suspects from the mostly Muslim republic of Dagestan - killed 34 and injured dozens.
Islamist insurgents based in North Caucasus republics such as Dagestan who are seeking their own independent state have vowed to disrupt the Sochi Games in order to undermine Russian President Vladimir Putin.
"The threats are real. They are basically calling for attacks on the Olympics. I think you're going to see attempts to do that," said Michael McCaul, chairman of the House Homeland Security Committee.
The Republican, in an interview from Moscow with ABC's "This Week," said Russian authorities were taking the threats seriously, deploying 100,000 security officials to erect a "ring of steel" to secure the Sochi airport, mountain trains and the Games themselves.
If there were attacks, he said, they would more likely be directed at soft targets like transportation.
The congressman added that the diplomatic security corps said it was getting good cooperation from the Russians, and noted that two dozen FBI agents were assigned to the massive sports event.
But "it could be a lot better. I want to press that while here," he added, saying he wanted to know more about emergency evacuation planning.
Another key congressman, House Intelligence Committee chairman Mike Rogers, said Russian authorities were clearly concerned about security.
"But we don't seem to be getting all of the information we need to protect our athletes in the Games," he said on CNN's "State of the Union."
Rogers, also a Republican, said the Russians' unwillingness to share information with US intelligence was "a departure of cooperation that is very concerning to me."
"So what we're finding is they aren't giving us the full story about what are the threat streams, who do we need to worry about," the lawmaker said.
"Are the terrorist groups who have had some success, are they still plotting?"
"There's a missing gap and you never want that when you're going into something, I think, as important as the Olympic Games," he added.
The Games open February 7 in Sochi, a resort city on the Black Sea coast.
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