WASHINGTON – A top U.S. counterterrorist official says there are "a number of specific threats" aimed at this week's Winter Olympics in Sochi, Russia — with the greatest danger coming from the Caucasus Emirate, which has threatened to attack the games.

Matthew Olsen, director of the National Counterterrorism Center, told Congress Tuesday that the U.S. and Russia are tracking threats of "varying degrees" of credibility.

He said potential attacks seem more likely outside the venues for the games, and instead in the area or region around Sochi. He described intelligence sharing with Russia as "good."

FBI Director James Comey said U.S. cooperation with the Russian Security Service has improved.

Russia has mounted a massive security operation, deploying more than 50,000 police and soldiers amid threats from Muslim insurgents.

The White House said President Obama received an update on security for the Olympics on Tuesday in the Situation Room. Vice President Joe Biden, Secretary of State John Kerry and CIA Director John Brennan were among the officials taking part. Leaders from the FBI and the Pentagon also joined.

Some lawmakers have raised concerns about safety at the Olympics and cooperation with Russia. FBI Director James Comey told a Senate panel last month U.S. cooperation with the Russian Security Service has improved.

Russian President Vladimir Putin's personally promised "ring of steel" to secure the Olympics is taking shape.

Armed soldiers in hooded green parkas stood guard Tuesday at the end of one runway at the Sochi Airport, where Olympic athletes, spectators and foreign dignitaries are beginning to arrive.

A camouflaged anti-aircraft station rests atop a hill nearby the cluster of ice events stadiums at the Winter Games' Black Sea coastal venue.

Sochi is beginning to resemble a police state, and that's just fine with the Olympic athletes, fans and locals.

"I feel pretty good about it, I mean they are trying as hard as they can," said U.S. bobsled pusher Chris Fogt, an Army captain who worked in intelligence and security in Iraq after the 2010 Vancouver Winter Olympics. "Something happened in Atlanta in '96, it can happen here. You just hope. I think that they are trying their hardest and they are doing everything they can."

British short track speed skater Jon Eley said: "The security is good, not over the top, and we feel safe."

The safety of the athletes could be tested, as two members of Austria's Olympic committee reportedly received a letter containing threats to kidnap skier Marlies Schild and skeleton competitor Janine Flock at the Winter Games, which officially open Friday.

Terrorist threats, the proximity of Sochi to troubled spots like Chechnya, and the general angst of hosting a large-scale event in the post-9/11 age have unnerved some people to the point of staying away from the Games.

A poll released Tuesday by the Pew Research Center found that 44 percent of Americans believe that holding the Winter Olympics in Russia was a bad idea, while 32 percent thought it was a good decision.

After hearing concerns about Sochi security from Washington and other world capitals, Putin made his vow to encircle Sochi in a "ring of steel" to discourage or thwart any terrorist activity.

From the looks of things, he's trying to deliver on his promise.

The Olympic Park and Olympic Village railway stations — critical transportation hubs for moving people from the coastal region to the mountain events — look more like airports than rail terminals.

The number of police officers, soldiers and Russian Cossacks walking beats at the stations has grown in recent days. A security force of 40,000 — police officers, military and Federal Security Service agents — are expected to descend on this city of 400,000 for the Games.

Passengers must go through metal detectors, have their bags X-rayed, and have suspicious contents examined before gaining entry to the stations. If the metal detectors go off or something doesn't look or feel right, stern-looking security officials donned in purplish patchwork quilt-style warm-up suits are at the ready to provide a thorough pat down.

There's been an increase in recent days in the number of police officers and soldiers who stroll the aisles of passenger trains. Recordings in English and Russian over the train's loudspeakers urge passengers to watch out for and report suspicious items.

Television cameras monitor the tracks along the high-speed rail line to mountainous Krasnaya Polyana. And security forces were stationed under the rail route's bridges and the underpasses of the highway next to the tracks.

The McClatchy Washington Bureau contributed to this report.