Though the investigation remains unfinished, Defense Secretary Donald H. Rumsfeld issued a statement in support of Franks.
The Pentagon's inspector general has been looking into charges that Franks allowed his wife, Cathy, to sit in on highly classified briefings and may not have properly reimbursed the government for travel expenses when she accompanied him on some trips, defense officials said on condition of anonymity.
An unidentified source also told the Washinton Post that a female soldier allegedly was assigned to assist Franks's wife on an almost full-time basis and that Cathy Franks was given a military bodyguard.
Army Lt. Col. Gary Keck, spokesman for the inspector general, declined to comment on details of the probe, as did the U.S. Central Command, which Franks heads.
"I am aware of the investigation and am cooperating with it," Franks said in a brief statement. "It would not be appropriate to comment on the investigation until it is complete."
The charges were made by a subordinate, and two senior members of the Central Command staff declined to act on the complaints before they eventually were taken to the inspector general, according to the Post, which first reported the investigation in Tuesday's editions.
It was unclear what, if any, disciplinary action might follow from the probe of Franks, a key figure in the government's war on terror as well as preparations to disarm Iraqi President Saddam Hussein by force if necessary.
Citing an unidentified source, the Post said the inspector general would probably reject most of the allegation as unfounded, but would conclude some charges, including those related to briefings and travel expenses, may require some sort of official disciplinary action.
The newspaper also said such investigations of generals are not unusual.
Rumsfeld issued a statement calling Franks an "enormously talented commander."
"Investigations such as this are not unusual and properly are required whenever the Office of the Inspector General is made aware of an allegation," Rumsfeld said. "Without commenting on the merits of the investigation, which is not yet before me, I want to emphasize that General Franks has my full trust, respect and confidence."
The 57-year-old Texas native is highly decorated from his service, including in Vietnam and the 1991 Persian Gulf War, with five bronze stars, three purple hearts and two distinguished service awards.