The federal prosecutors said in the three-page filing that they backed the president’s request for a temporary delay on the subpoena so that they could decide whether the government would offer an opinion on the “weighty constitutional issues” raised by the president’s lawyers.

“In view of those constitutional issues and the federal interests that they may implicate, the United States is currently considering whether to participate,” the office wrote.

The prosecutor’s office did not take a position on the merits of Mr. Trump’s argument.

It was unclear why the government chose to weigh in so late on a case in which it has had no formal role. But any potential involvement by the United States government would normally be approved, if not initiated by, the Justice Department in Washington.

The filing came the night before the judge, Victor Marrero of Federal District Court in Manhattan, heard 90 minutes of arguments on the president’s effort to stay the subpoena. At the end of the hearing on Wednesday, the judge gave the government until Monday to decide if it would wade into the case and until Oct. 2 to file a brief. He also delayed the enforcement of district attorney’s subpoena for a day.

“I would suggest that the parties go home, sober up and decompress,” Judge Marrero said, suggesting that they get together in the next day to try to resolve their concerns.