Popkov said one woman was summoned to go to the police station but "later they told her: I see you are not an extremist, you don't have to come."
Andrei Soldatov, an independent Moscow-based security analyst, described the police raids as a throwback to Soviet times.
"They follow the Soviet methods while working to ensure security, trying to establish control over activists and dissenters," he said. "Control is a key word for them, but it's not synonymous with security."
Soldatov said jihadists fighting to carve out an independent Islamic state in the Caucasus could have placed sleeper agents in Sochi years ago.
"The probability of that is quite high, they had plenty of time to prepare," he said.
Shvedov, the Caucasian Knot editor, agrees.
"If they wanted to get explosives in Sochi, they could have done it well before the attacks in Volgograd, when massive construction work was underway and there was little control over people who flowed into the city," Shvedov said.