The FSB said in a statement it had "thwarted the illegal activities of ... the international terrorist organisation Islamic State" on September 30, by detaining all members of a cell in the Moscow region.
It said they were all from Muslim-majority republics in the Caucasus but took orders from "foreign emissaries" pledging allegiance to the IS.
The group was planning "significant" terror acts in Russia, including in densely populated places and on public transport, the statement said, without specifying the number held.
Russian officials regularly claim foiling terror plots. In August, the FSB said it had arrested four IS members who were planning suicide attacks in Moscow shopping malls.
In July, security services said they arrested seven Central Asian migrants accused of preparing attacks in St Petersburg, where 15 were killed in a metro bombing in April claimed by a little known group called the Imam Shamil Battalion.
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