WASHINGTON — Defense Secretary Mark T. Esper on Sunday demanded the resignation of the Navy secretary, Richard V. Spencer, declaring that he had lost “confidence” in the Navy’s top civilian leader after Mr. Spencer diverged from President Trump over the treatment of a member of the Navy SEALs at the center of a high-profile war crimes case.

In a statement, Mr. Esper said he had lost trust in Mr. Spencer because his private statements about the Navy SEAL case differed from what he advocated in public. But Defense Department officials said Mr. Spencer prompted the ire of Mr. Trump when he threatened to resign over the president’s handling of the case of the SEALs member, Chief Petty Officer Edward Gallagher, and publicly said he disagreed with the president’s handling of the matter.

“I wish Richard well,” Mr. Esper said in a statement on Sunday. He added that he was “deeply troubled by this conduct shown by a senior D.O.D. official.”

The ousting of Mr. Spencer, first reported by The Washington Post, is the latest turn in an extraordinary story of how Mr. Trump has angered and alienated his own senior military leadership over his interference in how three American service members accused of war crimes have been treated.