The FBI is a federal law enforcement agency of the Department of Justice. The letters FBI stands for Federal Bureau of Investigation. Its main location is in the J. Edgar Hoover Building, located in Washington, D.C. It was established by J. Edgar Hoover, who was the director of the FBI from 1924 to 1972.
In the back of the book, there is a note saying to all FBI agents to impersonate Cahill family members in order to find out more about the 39 Clues. This plan is later revealed in Rapid Fire 2 when a Vesper impersonated Cousin Ingrid during Grace's will reading. Cahills vs. Vespers Mission 0: The Acropolis Raid
It is possible that the Vespers control the FBI because when you search Vespers in the FBI database it deletes all your files.