(CNN) -- A video surfaced Sunday threatening the Winter Olympics. Russia's President Vladimir Putin vowed the Games will be safe, but some U.S. lawmakers warn that they won't be.
One thing was clear as debate over the situation surged on Sunday: security is a top concern, less than three weeks away from the competition.
"It's a very serious fear," Sen. Angus King, I-Maine, told CNN Sunday.
Putin acknowledged that the Games, like any high-profile event, could be a target for terrorists.
But, he said, Russia has a "perfect understanding" of the threat and how to stop it.
As a transcript of his interview with half a dozen national and international broadcasters was posted on the Kremlin website Sunday, a video that surfaced online again highlighted the security situation.
In the video, posted on a well-known Jihadi forum website, two young men believed to have been suicide bombers in last month's back-to-back bombings in the Russian city of Volgograd speak of those attacks and make an ominous promise.
"We've prepared a present for you and all tourists who'll come over," the video says. "If you will hold the Olympics, you'll get a present from us for the Muslim blood that's been spilled."
In the video, the men are dressed in black and standing in front of a black banner with religious verse that is typically associated with al Qaeda-linked extremists.
Last month's attacks in Volgograd, a major transit hub about 650 kilometers (400 miles) away from Sochi, sparked concerns over security as the Olympics approach.
The explosions targeted a train station and a trolley bus and claimed the lives of more than 30 people.
In addition to the Volgograd attacks, there has also been violence in recent days in the southern republic of Dagestan -- the latest unrest linked to a long-running Islamist insurgency in the North Caucasus region.
Putin has pledged that visitors to Sochi for the Winter Olympics will be kept safe.
"We will try to make certain that the security measures are not intrusive or too conspicuous, so they are not too noticeable for the athletes, the Olympics' guests or journalists," Putin said, according to the interview transcript.
"But at the same time, we will do our utmost to ensure that they are effective."
Russia has plenty of experience in keeping international events secure, Putin said, pointing to the G8 and G20 summits as examples.
"Security is to be ensured by some 40,000 law enforcement and special services officers," he said. "Of course, we will draw on the experience acquired during similar events held in other regions of the world and in other countries. It means that we will protect our air and sea space, as well as the mountain cluster."
But several U.S. lawmakers offered a different take Sunday on CNN's State of the Union.
King, a member of the Senate Intelligence Committee, said he wouldn't go to the games himself, "and I don't think I would send my family."
Rep. Mike Rogers, chairman of the House Intelligence Committee, also called on the Russian government to be more cooperative with the United States on intelligence sharing ahead of the games.
"Their level of concern is great, but we don't seem to be getting all of the information we need to protect our athletes in the Games. I think this needs to change, and it should change soon," Rogers said.
When asked whether he thought Americans would be safe at the Games, former CIA and NSA director Michael Hayden said he trusts Russia's ability to provide security.
"I think Americans will be quite safe," he said.