WASHINGTON — Hillary Clinton’s chief of staff at the State Department said in sworn testimony released Tuesday that Mrs. Clinton’s advisers gave little thought to the problems her private email server might create if they were forced to turn over her communications under public records law.

“Certainly from my standpoint, I wish that had been something we thought about,” Cheryl D. Mills, who was chief of staff when Mrs. Clinton was secretary of state, testified in a deposition on Friday in a lawsuit against the State Department brought by a conservative legal group.

Ms. Mills’s comments — contrite at times, defensive at others — represented the first sworn public accounting from a member of Mrs. Clinton’s inner circle about the controversy over her exclusive use of a private email account during her State Department tenure.

The issue, which has dogged her presidential campaign for more than a year, flared up again last week after the release of a highly critical investigation by the State Department’s inspector general that found Mrs. Clinton was not authorized to use the private server. Mrs. Clinton declined to be interviewed for that inquiry.