By Li Hongmei

Russian police have killed a senior Islamist militant in Russia's North Caucasus ahead of the Winter Olympics in Sochi, where security forces searched on Tuesday for a woman they fear is planning an attack during the games.

Eldar Magatov, a suspect in attacks on Russian targets and alleged leader of an insurgent group in the Babyurt district of Dagestan, died in a shootout, the National Anti-Terror Committee said on Tuesday.

President Vladimir Putin has pledged to hold a successful Olympics and has therefore tightened security nationwide after terrorists threatened to attack the games, which start on February 7.

Putin had a phone call on Tuesday with U.S. President Barack Obama in which they discussed how best to have a "safe and secure" Winter Olympics, the White House said.

In Sochi, which plans to host hundreds of thousands of visitors during the games, security forces were searching for Ruzanna Ibragimovaya, 23, who may have arrived to the Olympic host city on January 11-12.

"(She) may be used as a terrorist-suicide bomber by (insurgency) leaders to organize terrorist acts during preparations for and during the 2014 Winter Olympics," read the letter, asking police to look immediately into the matter.

The letter from Russia's Federal Security Services to local police said she was the widow of a slain Islamist militant and is believed to have recently left her home in Dagestan, which lies nearly 600 km (370 miles) from Sochi on the opposite end of Russia's predominantly Muslim North Caucasus region.

Photographs of Ibragimovaya show a woman in a hijab, wearing a long dress.