"The command of the Vilayat Dagestan mujahedeen... declares that the Caucasus fighters are not waging any military activities against the United States of America," the Kavkazcenter.com website used by Russia’s North Caucasus jihadist movements said Sunday. “We are only fighting Russia." US media report the FBI is studying possible ties between the two main suspects Dzhokhar and Tamerlan Tsarnaev and violent Caucasus Islamist movements.