MOSCOW — Russia sent troops across Dagestan on Tuesday as the government pressed an offensive against insurgents and new threats emerged weeks before the Winter Olympics kick off in the Black Sea resort of Sochi.

MOSCOW — Russia sent troops across Dagestan on Tuesday as the government pressed an offensive against insurgents and new threats emerged weeks before the Winter Olympics kick off in the Black Sea resort of Sochi.

Two counter-terrorism operations were under way in Dagestan, a Muslim-majority region on the Caspian, east of Sochi, said Alexander Polyakov, a spokesman for the National Anti-Terrorist Committee. Security forces also embarked on a third mission, surrounding a group of suspected militants in a house, Interfax reported, citing an unidentified local official.

Russian authorities are pushing to dispel concerns about deteriorating security in the region with less than three weeks left before the games in Sochi begin Feb. 7. The operations in Dagestan come on the heels of renewed threats against the Olympics made in a video released three days ago by Islamic extremists, who also claimed responsibility for suicide bombings in Volgograd that killed more than 30 people last month.

"As you understand, such videos do attract attention," Polyakov said by phone, adding that security experts were studying the recording. He said he couldn’t comment immediately on a Fox News report that Russia and U.S. security forces are searching for four potential female terrorists in Sochi.

Russia will do "whatever it takes" to prevent a terrorist attack at the Olympics, President Vladimir Putin said in an interview broadcast Jan. 19 on ABC’s "This Week" program. The authorities are taking "sufficient measures" to protect the event, Russian Foreign Minister Sergei Lavrov told reporters in Moscow Tuesday.

While the Olympics have added a new urgency to Russia’s two-decade-long campaign to put down an insurgency in the North Caucasus, the security crackdown risks further radicalizing the groups resisting federal forces, according to Tatyana Lokshina, program director in Moscow for Human Rights Watch, which Tuesday released a review of Russia as part of its World Report 2014.

An increase in abductions and the use of violent tactics by the authorities in Dagestan is damaging dialogue with local communities, creating fertile ground for Islamic insurgents to recruit new members, Lokshina said.

"As the Olympic Games in Sochi were approaching, the Kremlin became increasingly concerned with continuous violence in Dagestan, and wanted fast results," she said. "So its soft power tactics were replaced with the use of brutal force."

Russia is "using many forces and means" in Sochi, limiting the movement of people and goods in the region starting on Jan. 7, Putin said in an interview with foreign and domestic media recorded in Sochi Jan. 17. Russia is spending about 1.5 trillion rubles ($45 billion) to stage the games, making them the costliest Winter Olympics on record.

"We will protect our air and sea space, as well as the mountain cluster," Putin said in the interview. "I hope that it will be arranged so that it will not be evident and, as I have already said, will not depress the participants in the Olympic Games."

Sochi lies to the west of the Caucasus mountains, which stretch about 1,200 kilometers (745 miles) across Chechnya to Dagestan, one of Russia’s most economically distressed regions. Chechen rebels fought two wars against the federal government since 1994. The separatist movement grew into an Islamist insurgency that took its fight to neighboring provinces.

In a video posted on YouTube on Jan. 18, two Russian- speaking men identified as members of a militant group operating in Iraq are shown preparing explosives and promising "presents" for Putin and tourists during the Olympics.

A leader of an insurgent group in Dagestan was killed during one of the operations Tuesday, Interfax reported, citing the National Anti-Terrorist Committee. A homemade bomb uncovered near a government building in a Dagestani village was safely defused, state-run RIA Novosti reported.

Three suspected extremists were shot dead Monday in the regional capital of Makhachkala, two days after another seven militants, including one woman, were killed on the city’s outskirts, according to the news service.