The Air Force, already under fire for mishandling the remains of war dead at the mortuary in Dover, is being urged to seek an outside review of its investigators in response to criticism that the service fell short in its effort to hold people accountable.

Earlier this week, the Air Force announced that it had disciplined three officials after investigating whistleblowers’ allegations of “gross mismanagement” at the mortuary. An independent government watchdog agency set up to protect whistleblowers said, however, that the Air Force had managed to “stop just short of accepting accountability.”

“The Air Force basically tried to make the Air Force not look too bad,” said James G. Parsons Sr., one of the whistleblowers who contacted the watchdog, the Office of Special Counsel. “They did try to cover it up.”

The Air Force’s chief of staff, Gen. Norton A. Schwartz, has acknowledged the problems at Dover, telling reporters “there should be no misunderstanding” that he and the service’s civilian leader, Air Force Secretary Michael Donley, bear responsibility. In a letter, Donley noted that an independent panel has already been tasked with reviewing the adequacy of the measures the service has taken at the mortuary since the reports involving lost body parts and lax supervision.

But the contrition and corrective steps haven’t been enough to quiet calls for more action, including a review from congressional overseers.

On Thursday, Sen. Claire McCaskill (D-Mo.), a member of the Senate Armed Services Committee, wrote to Schwartz and Donley to call for a review of the Air Force’s Inspector General’s independence, saying the “mission of an IG cannot be compromised to protect the interests of an institution, as may have happened here.”

“The Air Force cannot address major failings in leadership and management with half-hearted corrective action and the assignment of limited individual responsibility. Accountability must be swift and decisive,” she wrote.

McCaskill again pressed the case at a hearing of military service chiefs on Thursday. Addressing Schwartz, she said acknowledged the steps the Air Force had taken so far, adding, “No one has to convince me that you want to get this right at Dover.” But she said she was concerned that the assignment of responsibility had been limited.

Schwartz did not respond to the request for an investigation. But he challenged McCaskill’s suggestion that the Air Force had not sought to hold people to account.

“There clearly were unacceptable mistakes made,” he said. “Whether they constitute wrongdoing is another matter entirely. And when you look at a situation like this, you look at the facts of the case, as an attorney might, you look at the context in which the mistakes occurred. And you also consider the demands that are placed on individuals and organization.”

He noted that the senior military officer at the mortuary had received a letter of reprimand — usually a career-ending punishment for an officer.

“This,” Schwartz said, “is not a trivial sanction.”