The chairman of the House Homeland Security Committee says there are "specific and credible" threats of terrorism at the Winter Olympics in Sochi, Russia, and fears a terrorist attack is likely.

"I've never seen a greater threat [at an Olympics], certainly in my lifetime," Rep. Michael McCaul, R-Texas, told "Fox News Sunday."

McCaul said terrorist threats are heightened because the games are being held "right dead center in the middle of what has been a historic battleground between Russia and the Chechen rebells."

"You've had the leader of the Chechen rebels, [Doku] Umarov, calling for attacks on the Olympics," the lawmaker said. "And then [Ayman] al-Zawahiri, the al Qaeda leader, the lieutenant of [Osama] bin Laden, reinforcing that threat.

"So that's a whole new ball game that make these Olympics very, very different."

Despite Russia deploying tens of thousands of security officials in a "ring of steel" around the Olympic site, McCaul said security officials worry that "black widow" female terrorists, so-called because some seek to avenge the deaths of their husbands who were killed by Russian authorities, may be able to slip past security measures to launch attacks.

The Sochi airport, which is inside the ring of steel, also is major security concern for officials, he said.

"I think there's a high degree of probability that something will detonate, something will go off, but I do think it is likely to happen outside of the ring of steel and the Olympic village," he said. "I hope I'm wrong."

McCaul said that while Russian officials are cooperating with U.S. security and counterterrorism agents regarding potential threats coming from outside Russia, the Russians have been less effective in dealing with threats inside the country. "That's where we'd like to work more closely with them."

Rep. Adam Schiff, D-Calif., a member of the House Permanent Select Intelligence Committee, agreed Russian officials haven't been forthcoming sharing intelligence information with the U.S.

"I think as a matter of Russian pride they don't want to share that," Schiff told "Fox News Sunday." "But it means that we're less effective in protecting our people, and that's a frustration."

Still, the Democrat said that "all things considered, it's relatively and manageably safe to be at the games.

"If people stay where they're supposed to and don't vary off into uncharted areas, minimize the time they spend in train stations ... I think the risks can be contained," Schiff said.

"I would go [to the Sochi games] if I had tickets."