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Putin has put security forces on high alert to safeguard the Games in the Black Sea resort of Sochi, which lies near to mainly Muslim southern provinces where Russia is battling an Islamist insurgency that has targeted Moscow.
"We must fight back hard against extremists who, under the banners of radicalism, nationalism and separatism, are trying to split our society," Putin said.
"The policy in the fight against corruption, crime and the insurgency has to be carried out harshly and consistently," Putin told a meeting of security force officers.
"The situation in the North Caucasus should be kept under particular control."
Friday's raid, the third targeting Muslim places of worship in Moscow or St Petersburg this year, led to the detention of 300 people including 170 foreigners and the confiscation of Islamist literature to check for extremist content, Russian news agencies quoted the Federal Security Service (FSB) as saying.
The FSB did not say why the people had been detained.
Russia is keen to boost its counter-terrorism credentials after the deadly Boston Marathon bombing allegedly carried out by two ethnic Chechen men, one of whom spent time last year in the North Caucasus province of Dagestan that borders Chechnya.
The Islamist insurgency, led by the 'Caucasus Emirate' group and Russia's most wanted man Doku Umarov, is rooted in two post-Soviet wars between Moscow and Chechen rebels. The insurgents want to create an Islamic emirate in the North Caucasus region.
Fears of Islamist militants in Moscow have risen since police killed two men and detained another two who allegedly belonged to an outlawed Islamist group that was plotting an attack during a major holiday earlier this year.
Human rights activists say Russia's Islamist insurgency is fuelled by a combination of religion, official corruption and strong arm tactics against suspected militants by local leaders.
In Dagestan, which has become the focal point for insurgent violence, police disarmed two suicide bomber belts and detained two women, Interfax reported on Friday.