The incident came a week before Russia's presidential election on March 18 and three months before the country hosts the 2018 World Cup.
"Following an investigation and searches in the region of Saratov, the FSB foiled a planned terrorist attack by members of a secret terrorist cell," the FSB said in a statement.
"There was an exchange of gunfire between the security forces and the criminals during which they were fatally wounded," it added, without specifying the number of people killed.
The security services also said they recovered pistols, homemade grenades and an explosive device with three kilos of TNT in Saratov, about 800 kilometers (500 miles) from Moscow.
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Russia has been targeted by the jihadist Islamic State group (IS) and the Syrian branch of al-Qaeda following the Russian military's intervention in Syria in 2015.
The Russian security services frequently announce the breaking up terrorist cells, often implicating people from the ex-Soviet republics in Central Asia.