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Militants on Sunday posted a chilling self-portrait video of the two Volgograd killers as they purportedly traveled to their targets. They made a direct threat on the Olympics.

“We’ll have a surprise package for you,” one of them said, according to ABC News. “And those tourists that will come to you, for them, too, we have a surprise. If it [the Olympics] happens, 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.”

Rep. Michael T. McCaul, Texas Republican, said the two belonged to Ansar al-Sunnah, an al Qaeda-linked group from Iraq.

“All the briefings I received from the intelligence community, to the FBI and others, indicate that there are serious concerns and that we need to do a lot to step up security,” Mr. McCaul told ABC News. “I do believe Putin is doing a lot of that. These are the largest security operations for any Olympic Games in the history of the Olympics.”

Umarov called on his followers to carry out attacks to disrupt the Olympics in any way.

“I think you’re going to see attempts to do that. I think it’s more likely that the attacks would probably happen outside of the perimeter in more soft targets, transportation modes, if you will,” said Mr. McCaul, who was en route to Sochi to survey security preparations.

Ken Allard, a retired Army intelligence officer, said the Russians have long experience in dealing with domestic terrorists.

“They have experience on both ends of that problem,” he said. “The KGB fought anti-Soviet separatists while also sponsoring terror against the West. So they can be a lot more ruthless than any Western democracy.”

Mr. Allard sad Mr. Putin has staked his reputation on keeping the Games insulated from terrorists and will do “the ruthless thing, if need be.”

“All that said, neither Soviets nor Russians have been completely successful against Chechen separatists, both for ideological and nationalist reasons. So I think Putin will do his best to lock things up,” he said. “And no, he may not be completely successful.”

Jacqueline Klimas contributed to this report.