Defense Secretary Leon E. Panetta on Thursday ordered the Air Force to review whether it had been tough enough in disciplining — but not firing — three supervisors at the Dover Air Force Base mortuary, saying: “Full accountability is what we intend to deliver.”

Panetta also said he had faith in Air Force Secretary Michael B. Donley, despite harsh criticism from lawmakers and an independent federal agency about the credibility of the Air Force’s 18-month investigation into missing body parts and mishandled remains at the Dover mortuary, which handles the remains of American troops killed overseas.

“I trust Mike Donley,” Panetta said during a news conference. “I think he tried to deal with this matter, to go after with the issues involved here, to correct them and to do whatever was necessary to deal with it.”

Panetta’s instructions came two days after he commended the Air Force for conducting a “thorough” investigation and said he agreed with the disciplinary actions it imposed. Asked what had changed, he cited a report issued by an independent federal watchdog, the Office of Special Counsel, which criticized the Air Force for being too lenient and not taking full responsibility.

Donley promised that his disciplinary review would be “exceedingly thorough and rigorous, as our fallen and the families they leave behind deserve nothing less.”

For the first time since the mortuary scandal erupted on Tuesday, Donley publicly expressed remorse for the problems.

“The lapses in our standards at Dover, which we sincerely regret, are our responsibility to fix,” he said in a statement. “I want to reassure our military family that our fallen are being treated, and will continue to be treated, with the utmost reverence, dignity and respect.”

Members of Congress, however, said they were appalled to learn that, in addition to losing body parts, the Dover mortuary had disposed of cremated portions in a Virginia landfill for several years.

“We must have an in-depth and detailed accounting of what happened,” said Rep. Rob Wittman (R-Va.), chairman of the investigative arm of the House Armed Services Committee. “Most importantly, we must ensure that this never happens again.”

Panetta said he was unaware of the landfill-dumping practice and hoped an independent panel of medical experts he has appointed to review the Dover mortuary operations would examine the issue.

Seated next to Panetta at a news conference, Gen. Martin E. Dempsey, chairman of the Joint Chiefs of Staff, noted that the mortuary stopped disposing of ashes in the landfill in 2008 and asserted that the practice was “not uncommon” outside the military.

“If you look into how it’s handled routinely in civilian life, there are procedures exactly that way,” he said.

Asked if it was morally objectionable or wrong to dispose of portions of troops’ remains in that manner, Dempsey replied: “I don’t know what right looks like in that regard now that this has manifested itself.”

An association of funeral directors, however, called the Dover mortuary’s landfill-dumping “horrific.”

“The disposition of the remains at a landfill violates every formal and informal professional standard for the respectful and dignified interment of the deceased,” the International Cemetery, Cremation and Funeral Association, which represents more than 7,500 funeral homes, cemeteries and crematories, said in a statement.

Military officials have defended the practice, saying it is similar to how hospitals dispose of medical waste. But Kenneth E. Varner, the president of the funeral association, said there was a big difference between how hospitals handle blood or amputated limbs from living patients and how they handle ashes from the dead.

“Of course, the difference is that hospitals are working to save lives, and the distinction should be obvious,” said Varner, who is also the chief executive of Cypress Lawn, a large cemetery and funeral home near San Francisco.

Also Thursday, Claire McCaskill (D-Mo.), a member of the Senate Armed Services Committee, asked the Air Force to review the independence of its inspector general, the agency that conducted the 18-month investigation into the Dover mortuary.

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

McCaskill pressed her request at a hearing of the military’s service chiefs on Thursday. Addressing Gen. Norton A. Schwartz, the Air Force’s chief of staff, she said she was concerned that the assignment of responsibility had been limited.

Schwartz 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.”

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.”

Two civilian supervisors at the mortuary have received a demotion in their pay grades and have been reassigned to other jobs.