The FSB said in a statement that its officers found five firearms, two improvised explosive devices, each with the equivalent of 10 kilogrammes of TNT, and various types of ammunition at the suspects' homes.
The FSB did not say if the arrests were made in Moscow or the region of Ingushetia in the North Caucasus where the men were believed to be planning attacks.
Islamist insurgency spread to Russia's Dagestan and Ingushetia in the early 2000s after the end of the war in Chechnya.