WASHINGTON — President Trump said on Monday that he would direct the Pentagon to establish a sixth branch of the armed forces dedicated to protecting American interests in outer space, an idea that has troubled lawmakers and even some members of his administration, who have cautioned that the action could create unnecessary bureaucratic responsibilities for a military already burdened by conflicts.

During a speech at a meeting of the National Space Council, Mr. Trump announced plans to protect American interests in space through monitoring commercial traffic and debris, initiatives he said would be “great not only in terms of jobs and everything else, it’s great for the psyche of our country.”

Minutes later, the president zeroed in on Gen. Joseph F. Dunford Jr., the chairman of the Joint Chiefs of Staff, and tasked him with the undertaking of creating another branch of the military.

“General Dunford, if you would carry that assignment out, I would be very greatly honored,” Mr. Trump said from the podium, after searching for him in the crowd.