The bust in the city of Nalchik, located about 300 kilometers (about 185 miles) east of Sochi, comes less than a month before the start of the 2014 Winter Olympics.
The National Anti-Terrorism Committee said the suspects belonged to an international terror group and were in possession of grenades, ammunition and a self-made explosive device. The agency didn't name the group the suspects allegedly belonged to or give further details.
The arrests follow back-to-back suicide bombings in the city of Volgograd in southern Russia, which killed 34 and wounded 100 others, on Dec. 29-30.
Security fears were further heightened Thursday when police found four cars with the bullet-riddled bodies of six men near the city of Pyatigorsk, about 275 kilometers (about 170 miles) northeast of Sochi across the North Caucasus Mountains.
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Explosive devices had been placed near three of the cars, although only one of the bombs went off and no one was hurt. Security forces in the region were scrambling to track down those responsible for those killings.
On Tuesday, authorities enacted a stringent security regime in Sochi barring entrance to all vehicles except for those registered in the city or with special Olympics passes.
President Vladimir Putin has personally overseen preparations for the Olympics, his pet project intended to showcase Russia's power and wealth. Last week, he inspected preparations for the games and went skiing in the mountains near Sochi.