(CNN) -- Russia's prime minister tried to reassure the world about the safety of the upcoming Olympic Winter Games on Tuesday as security forces worked to clamp down on potential threats far from the Black Sea resort where the games will soon begin.
A suspected militant leader died in a shootout with police in the restive Caucasus republic of Dagestan, hundreds of miles east of the Olympic venues in Sochi, the state news agency RIA Novosti reported. The news agency said Russian special forces were engaged in other operations in the same territory. And in Sochi and in Rostov-on-Don, a nine-hour drive to the north, police handed out posters of women they suspect may be planning terrorist attacks.
In an interview set to air Wednesday on CNN's Amanpour program, Prime Minister Dmitry Medvedev said "there are always some threats" to public events, "not only this country but also in others." But Russian authorities are aware of those threats and are planning accordingly, he said.
"I am referring to the mobilization, build-up, of police forces, and a huge number of policemen will watch the progress of the Games," Medvedev said.
Russia has been battling a low-level Islamist insurgency in Dagestan and the North Caucasus region for more than a decade, and militants have vowed to strike at the Games. Over the weekend, as President Vladimir Putin told reporters his government has a "perfect understanding" of the threat and how to stop it, a video posted online warned that the insurgents had "a present" for Olympic visitors.
U.S. may share counter-IED tech with Russia
Andrew Kutchins, the head of the Russia and Eurasia program at the Washington-based Center for Strategic and International Studies, said Putin made a "brazen bet" by bidding for the Games in Sochi.
"He sees one of the historic roles he has played as being to stabilize the North Caucasus. Unfortunately, the North Caucasus aren't as stabilized as he would like, and by holding the Sochi Olympics in such close proximity to, in effect, a conflict zone, he's taking a big risk. If things don't go well all of his claims about the stability he has brought to the North Caucasus -- and in a way, more broadly, to Russia -- are going to be diminished."
Kutchins said it would be "very, very difficult" for militants to pull off large-scale attacks in Sochi, but he said they don't have to hit Sochi itself to hurt the Games. A series of attacks like the Vologograd bombings in the surrounding area "would raise the terror level in the country and in the international community to such a level that the Games themselves would be imperiled," he said.
Amid the concerns, the top U.S. military officer discussed sharing high-tech equipment to counter improvised bombs with his Russian counterpart Tuesday, a Pentagon spokesman told CNN.
The matter came up "on an exploratory level" in a meeting between Gen. Martin Dempsey, the chairman of the Joint Chiefs of Staff, and Russian Gen. Valery Gerasimov, Dempsey spokesman Col. Edward Thomas said.
The United States developed portable and vehicle-mounted jamming systems after radio-controlled roadside bombs took a huge toll on American troops in Iraq and Afghanistan. A U.S. official with knowledge of the discussions said military staff from both countries will now look at whether the U.S. technology is compatible with Russian systems.
Fears of 'black widows' as Games near
In Sochi, police have handed out fliers at hotels warning of a woman they believe could already be in the city and planning a terrorist attack. One flier, dated January 15, 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.
Ibragimova may be involved in organizing "a terrorist act within the 2014 Olympic region," the flier warns. Authorities received information about Ibragimova's possible arrival in the region last week, it states.
CNN obtained the notice from security staff at a hotel in Sochi. Photos of Ibragimova have flooded television and social media reports from Sochi, and some describe her as a "black widow" -- a group of women who have carried out high-profile suicide bombings after their insurgent husbands were killed by government forces.
Security experts stressed Monday that Ibragimova was probably one of many suspects that authorities are trying to find. But former FBI agent Don Borelli said protecting the Games will require "multiple layers" of security.
"If somebody's already on the inside -- if she's already, let's say, has a job at a particular event or has special access, then she's already bypassed one of those layers of security," Borelli said. "Hopefully, now that this warning has taken place, they'll find her, if in fact she's in the region."
Another flier handed out by security forces to hotels in Rostov-on-Don, in southwestern Russia, names three women it says could carry out a suicide attack planned by militant groups between January 21 and 24, during the Olympic Torch Relay.
One of the three, Zaira Nizamudinovna Alieva, was killed in a gun battle over the weekend in Dagestan in which seven militants reportedly died. She had been trained to be a suicide bomber, RIA Novosti cited terrorism officials as saying.
The other two are named as Djannet Kurbanismailovna Tcakhaeva and Oksana Albertovna Aslanova. Pictures on the flier show two of the three women in Islamic head coverings, but the text warns that the women may not be dressed that way.
"Suspected terrorists may use regular clothing without any Islamic elements, e.g. no long dresses, no hijab, which makes it easier to blend into a crowd, and makes it easier to get access to large gatherings without being noticed," it says.
CNN's Barbara Starr, Phil Black, Laura Smith-Spark, Joseph Netto and Gena Somra contributed to this report.