In a brash assertion of presidential power, the 20-page letter — sent to the special counsel, Robert S. Mueller III, and obtained by The New York Times — contends that the president cannot illegally obstruct any aspect of the investigation into Russia’s election meddling because the Constitution empowers him to, “if he wished, terminate the inquiry, or even exercise his power to pardon.”

Mr. Trump’s lawyers fear that if he answers questions, either voluntarily or in front of a grand jury, he risks exposing himself to accusations of lying to investigators, a potential crime or impeachable offense.

Mr. Trump’s broad interpretation of executive authority is novel and is likely to be tested if a court battle ensues over whether he could be ordered to answer questions. It is unclear how that fight, should the case reach that point, would play out. A spokesman for Mr. Mueller declined to comment.