The president has previously made it clear that he believes the country should tread carefully when calling American troops to account for acts of war. Only last week, he announced on Twitter that the White House was reviewing the case of Maj. Mathew L. Golsteyn, a former Army Special Forces soldier charged with murder in the death of a Taliban bomb maker in Afghanistan. “We train our boys to be killing machines, then prosecute them when they kill!” Mr. Trump wrote.

The issue in Chief Gallagher’s case became apparent to Admiral Green’s team in August, when the chief’s lawyers — including one of Mr. Trump’s personal lawyers, Marc Mukasey , who joined the defense team two months before the June court-martial — had tried and failed to persuade Navy commanders to suspend any punishment. Soon after that, the president brought up the Gallagher case at a meeting with the Secretary of the Navy and the Chief of Naval Operations, according to a senior Navy official.

White House officials strongly denied that the Gallagher case was discussed. But hours after the meeting, the Chief of Naval Operations announced that he would personally take over the Gallagher case from another admiral, who had indicated that she planned to punish the chief.

The Navy had also planned to discipline two other SEALs who had come under investigation in the Gallagher case: Lt. Jacob Portier, who was charged with not reporting Chief Gallagher’s actions in Iraq; and Special Operator First Class Corey Scott, a platoon medic whose testimony at the chief’s trial prompted the Navy to open a perjury investigation. But the day after the White House meeting, the charges against Lieutenant Portier were dropped and the investigation of Special Operator Scott was ended.

The intervention from Washington left Navy leaders with a dilemma: Not punishing Chief Gallagher and the others would undermine efforts to restore discipline in the ranks, but punishing them only to be publicly reversed might make things even worse.

“All that’s off the table now,” said a Navy Special Warfare officer who was briefed on the most recent deliberations of Admiral Green’s team about the matter. Navy commanders grew concerned that if they took away from Chief Gallagher the Trident pin that signifies membership in the SEALs, only to see the president give it back again, the officer said, “it sends a message that the commanders aren’t in control.”

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While taking no action against Chief Gallagher, the Navy recently fired two senior leaders of the team on which Chief Gallagher serves, SEAL Team 7, which has had other recent incidents of misconduct. The command cited a “loss of confidence that resulted from leadership failures.”