The FSB said the suspects were preparing attacks with automatic weapons and explosives in crowded places.
Security operatives confiscated a large quantity of firearms, ordnance and components to make improvised explosive devices, the FSB said in a statement.
Terrorists in Dagestan have mounted frequent attacks on police and officials, and some have sworn allegiance to Daesh.
The security services have in recent weeks announced several operations that thwarted potential attacks in Moscow and the second city Saint Petersburg.
In the wake of the recent killing of Moscow`s ambassador in Ankara and the truck attack on the Christmas market in Berlin, Putin ordered security bolstered.
Authorities in Moscow have said they will step up measures to protect revellers at New Year festivities, including using lorries to block potential vehicle attacks.
Russia has waged an air campaign in Syria since September 2015 in support of the Assad regime. President Vladimir Putin and other Russian officials have said that thousands of citizens of Russia and other ex-Soviet nations have joined Daesh Syria.
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