More than 57,000 patients have been waiting more than three months for medical appointments at hospitals and clinics run by the Department of Veterans Affairs, and nearly 64,000 others have been enrolled in the system for a decade but have still not been seen by doctors despite their requests, according to a nationwide audit released Monday.

The audit of the 731 facilities, including all of the department’s 150 medical centers, provided for the first time a sense of the scope of the widening scandal over delays in care within the sprawling health care system for veterans. The audit, conducted by the department, concluded that in 76 percent of the department’s hospitals and clinics, there had been at least one instance of manipulated data on patient wait times, in many cases to hide delays in providing care.

The audit also found that 13 percent of patient schedulers said that they had been instructed by “supervisors or others” to enter false information related to how long veterans had to wait for appointments. Of the 731 facilities that were part of the audit, 112 have been flagged for further review.