“I should not have been there,” Gen. Mark A. Milley, the chairman of the Joint Chiefs of Staff, said in a prerecorded video commencement address to National Defense University. “My presence in that moment and in that environment created a perception of the military involved in domestic politics.”

His first public remarks since Mr. Trump’s photo op, in which federal authorities attacked peaceful protesters so that the president could hold up a Bible in front of St. John’s Church, are certain to anger the White House, where Mr. Trump has spent the days since the police killing of George Floyd in Minneapolis taking increasingly tougher stances against the growing movement for change across the country.