Investigators said that Russell Little, 40, had also spoken about wanting to kill former Democratic Congressman Ben Chandler.
Barr defeated Chandler in 2013 for the Central Kentucky seat.
According to the FBI, Little repeatedly called Barr’s office in Lexington during a time span of five months.
Investigators said Little made explicit and direct threats during the calls.
The FBI said Little also called Barr’s office on August 4th and cursed while expressing his anger with Barr and Chandler.
State Police said they arrested Little later that day.
Troopers reportedly found a loaded .38-caliber pistol in the front passenger seat of his car.