"We are aware that the attorney general is required to travel by government aircraft for security purposes," they wrote. "However, based upon information provided to us, it is our understanding that the FBI pays for the attorney general's travel despite the fact that he has his own travel budget.
"If true, this travel would place unnecessary budgetary pressure on the FBI and may adversely impact the operational readiness of the FBI's air operations."
The letter poses several questions, including what percentage of FBI aircraft have been used for executive transportation, investigative operations and training for the last five years. It also asks how many investigative operations were unfulfilled for any reason, and requests that the details of those flights be shared with Congress.
Republicans on the letter said they understand that Holder has at times reserved FBI planes but then made other arrangements, leaving the plane idle.
"These allegations were particularly troubling because they suggested the FBI had to lease another plane to ensure the availability of aircraft for FBI operations," they wrote. "If these allegations are true, describe in detail each such instance where the FBI had to lease an additional plane due to Justice Department executive travel."
They also asked why the FBI pays for the attorney general's travel, whether Holder reimburses the FBI for personal travel and how much Holder has billed the FBI for executive travel.
The four Republicans asked Mueller to respond to these questions by Sept. 7.