They also argued that taking trophy photos with dead bodies is a relatively common practice in the military that, while illegal, is rarely prosecuted, and that the Navy had targeted the SEAL unfairly.

“Chief Gallagher faces a draconian punishment that does not fit the conduct,” Mr. Parlatore wrote in a request for clemency. “It will inflict unnecessary and irreparable harm on his wife, children, and the equity of the military justice system.”

The pleas for leniency were initially rebuffed over the summer by the convening authority in the case, Rear Adm. Bette Bolivar, the commander of Navy Region Southwest. In a letter to Mr. Parlatore, Admiral Bolivar said that she found Special Operator Gallagher’s behavior after his trial reprehensible, and that she had no intention of reducing his sentence.

Mr. Trump then called the Chief of Naval Operations at the time, Adm. John M. Richardson, to a White House meeting where Special Operator Gallagher’s case was discussed . Admiral Richardson took authority over the case from Admiral Bolivar a few days later; it passed to Admiral Gilday when Admiral Richardson retired in August.

Admiral Gilday’s decision to reduce Special Operator Gallagher by only one rank will still cost the SEAL nearly $200,000 in retirement pay, according to his lawyers’ estimate. And the SEAL could still face administrative punishment for other misconduct, according to a government official, including the loss of his Trident pin, which would signify he is no longer a SEAL.

Military lawyers say that clemency is nearly always requested after a court-martial conviction, but it is rarely granted, and that having the top admiral in the Navy take over authority for a case is nearly unheard-of.

“In my 15 years of military law, I’ve never seen it,” said Patrick Korody, a former Navy prosecutor who has followed the Gallagher case. “But there is a feeling among military lawyers that the defense has just steamrolled everyone below, so giving it to the C.N.O. is the right decision. He has authority to do the proper thing.”