(CNN) -- New details fueled debate Monday over security at the upcoming Winter Olympic Games in Sochi: Wanted posters of a terrorism suspect on the loose, warships at the ready and a video threat from beyond the grave.
Russian President Vladimir Putin stressed that his country has stepped up security and is prepared to handle any threats.
But some U.S. lawmakers -- and at least one Olympic athlete -- have said they're worried about the situation.
Hotels warned about terror suspect
Police in Sochi have handed out fliers at area hotels warning of a woman they believe could be a terrorist and who may currently be in the city.
One flier, obtained by CNN, asks workers to be on the lookout for Ruzanna "Salima" Ibragimova, described as the widow of a member of a militant group from the Caucasus region.
The woman, according to the flier, may be involved in organizing "a terrorist act within the 2014 Olympic region."
CNN obtained a copy of the flier, which is dated January 15, from security staff at a hotel in Sochi. The flier claims authorities have received information about Ibragimova's possible arrival in the region last week.
Photos of Ibragimova have flooded television and social media reports from Sochi. Some describe her as a "black widow" -- a notorious type of terrorist that's emerged in Russia's clashes with Chechen separatists.
Many of them are wives of insurgents killed by government forces, and they've been blamed for high-profile suicide bombings.
Security experts stressed Monday that the woman is likely one of many suspects authorities are trying to find.
"I guarantee they're talking about this one black widow," former CIA officer Mike Baker said, "but there are others that they're also worried about."
Official: U.S. military at the ready as contingency plan
The U.S. military will have up to two warships and several transport aircraft on standby under a contingency plan to help evacuate American officials and athletes from the Winter Olympics, if ordered, a U.S. official said Monday.
The State Department would take the lead in organizing and evacuating Americans, if necessary, the official with direct knowledge of the plan told CNN.
Moscow would have to ask for such assistance before the United States would act, the official said.
But planes and ships are clearly there "if something happens like a major terrorist attack and we need to get Americans out," the official said.
U.S. contingency planning calls for warships to launch helicopters to Sochi from the Black Sea. C-17 transport aircraft would be on standby in Germany and could be on the scene in about two hours.
Other aircraft contracted to the State Department would also play a role in any emergency.
A video threat from beyond the grave
In a video that surfaced Sunday, two young men believed to have been suicide bombers in last month's back-to-back bombings in the Russian city of Volgograd made 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."
The video was posted on a well-known jihadi forum website Sunday and apparently was recorded before the Volgograd attacks, which targeted a train station and a trolley bus and claimed the lives of more than 30 people.
Putin pledges stepped up security
Putin has pledged that visitors to Sochi for the Winter Olympics will be kept safe.
Russia has plenty of experience in keeping international events secure, Putin said, pointing to the G8 and G20 summits as examples.
Access to Sochi is under heavy restriction ahead of the games, and Putin said Sunday in an interview with half a dozen Russian and international broadcasters that about 40,000 members of Russia's police and security forces would be guarding events.
Security analysts have warned that terrorists targeting the Games may try to strike elsewhere in Russia during the Olympics.
U.S. lawmakers: Games won't be safe
U.S. Sen. Angus 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.
In recent weeks, U.S. law enforcement agents have been conducting interviews with people in the United States with ties in the Caucasus region, CNN has learned.
The region, which includes Dagestan and Chechnya, has been the scene of unrest and is in southern Russia, hundreds of miles from the venue of the Games.
The interviews are informational and do not mean there are any particular threats being investigated, a U.S. official said.
Law enforcement officials do "knock and talk" visits to meet people and to identify any potential issues. FBI agents conducted similar visits after last year's attack at the Boston Marathon.
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.
Will security concerns impact athletes?
Over the weekend, at least one Olympic athlete said he was worried.
"My concerns with Sochi is safety in a way, because it's in a crazy war zone in a way," French snowboarder Xavier de la Rue said. "It's in the middle of all these countries that want to kill Russia, so it's just scary 'cause I know that we're going to be a target in a way, although they do very well their job at keeping it safe but yeah, that's something that scares me a bit."
Tara Lipinski, who won a gold medal at the 1998 Winter Olympics and will be attending this year's games, said she feels safe -- and hopes competitors will, too.
"There have been so many threats at the Olympics," she told CNN Monday. "I think athletes are used to that, and they know that, OK, we're going to hear about this. But when we go, we have people that are surrounding us and telling us where we should be and where we shouldn't be. And hopefully they do feel safe."
CNN National Security Analyst Frances Fragos Townsend described the security climate in Sochi as "the most dangerous threatened environment that we've seen for the Olympics."
But she said competitors shouldn't have to worry.
"They'll go to real extremes to protect the athletes and the venues. ... There's a big falloff, though, when you talk about the families and the tourists," Townsend said. "There really is, I think, a far greater vulnerability."
CNN's Zarifmo Aslamshoyeva, Alla Eshchenko, Evan Perez, Olivia Yasukawa and Brooke Baldwin contributed to this report.