The brief took pains to say that there was nothing unusual about the department’s participation in the case, noting that it had previously filed friend-of-the-court briefs in cases in which Presidents Richard M. Nixon and Bill Clinton had claimed immunity in civil suits.

“The United States has a substantial interest in protecting the office of the president and the powers and duties vested in that office,” the brief said. “The United States also has a substantial interest in protecting the autonomy of the federal government from potential interference by the states.”

The subpoena from the Manhattan district attorney, Cyrus R. Vance Jr., a Democrat, threatened both interests, the brief said. “This case involves the first attempt in our nation’s history by a local prosecutor to subpoena personal records of the sitting president of the United States,” the brief said.