Sean Spicer, the White House press secretary, said Sunday that Mr. Bannon’s past service as a Navy officer merited his attendance at all meetings, as part of a “streamlining” of decision-making. He did not explain the downgrading of the four-star general who heads the Joint Chiefs, Joseph F. Dunford Jr., who rose through the Marine Corps and served in Iraq and Afghanistan.

“Well, he is a former naval officer,” Mr. Spicer said of Mr. Bannon on ABC’s “This Week.” “He’s got a tremendous understanding of the world and the geopolitical landscape that we have now.”

He added, “Having the chief strategist for the president in those meetings, who has a significant military background, to help make, guide what the president’s final analysis is going to be, is crucial.”

When pressed on General Dunford’s role, Mr. Spicer said, “The president gets plenty of information from the chairman of the Joint Chiefs of Staff.”

Current and former military officials said they suspected that the decision, in part, was prompted by the national security adviser, Michael T. Flynn, who retired as a three-star general after he was dismissed during the Obama administration as the head of the Defense Intelligence Agency. It was the previous director of national intelligence, James R. Clapper, who delivered the news to Mr. Flynn that he was being removed from his post.