The National Anti-Terrorist Committee said the militants killed in the majority-Muslim North Caucasus region of Dagestan were possibly linked to an attack on a local restaurant in which 16 people were injured last evening.
"Seven militants were killed," a spokesman for the anti-terrorist committee told AFP, noting that a senior local militant and a young woman who was allegedly trained to become a suicide bomber were among the dead.
The Saturday sweep was conducted in the main Dagestani city of Makhachkala where a car bomb went off near a restaurant last evening.
As a result of the bombing, 16 people were wounded including police officers, the Investigative Committee said in a separate statement.
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Twin attacks are a signature tactic of militants who are fighting to carve out their own state in the North Caucasus and pledged to strike the Winter Games in Sochi which begin on February 7.
President Vladimir Putin has repeatedly vowed to ensure safety during the Games in the Black Sea resort which has gone into unprecedented security lockdown mode.
"If we betray weakness, betray fear -- display our fear -- then we will be helping terrorists achieve their goals," said Putin.
Besides Dagestan and Ingushetia, North Caucasus includes Chechnya where Russian forces have fought separatists for the past 20 years.
The impoverished, corruption-infested region is the site of regular attacks on officials but the violence has recently been spilling outside the North Caucasus.