If Mr. Trump refuses to be interviewed, Mr. Mueller could subpoena him to answer questions in front of a grand jury. Mr. Giuliani said that if Mr. Trump cannot be indicted, he does not believe Mr. Mueller can subpoena him. “We would say they can’t,” Mr. Giuliani said. Mr. Trump’s lawyers believe that the only topic on which Mr. Mueller could seek to subpoena the president would be for information he personally had about obstruction of justice.

Mr. Mueller, who was appointed a year ago Thursday, does not appear to have gone that far in his views. But the fact that he has decided he will not indict the president before he has finished investigating the case strongly suggests that his reason has to do with the rules, apart from what the evidence turns up.

While nothing in the Constitution or federal statutes says that sitting presidents cannot be indicted, and no court has ever ruled that they are temporarily immune, lawyers with the Justice Department’s Office of Legal Counsel have twice concluded — once during the Nixon administration, and again during the Clinton administration — that the Constitution bars prosecuting presidents.

Both the stigma of being charged with a crime and the burden of a trial — including a likely need to be in the courtroom at times — would undermine the president’s abilities to carry out his duties, preventing the executive branch “from accomplishing its constitutional functions” in a way that cannot “be justified by an overriding need,” as Robert G. Dixon Jr., then the head of the Office of Legal Counsel, wrote in September 1973.

That theory — crafted by lawyers appointed by Presidents Richard M. Nixon and Bill Clinton — has been contested by some scholars. In particular, lawyers working for the special prosecutor in the Watergate case, Leon Jaworski, and the independent counsel in the Whitewater and Monica Lewinsky investigations, Kenneth Starr, maintained that the Justice Department’s interpretation was wrong and that a president could be indicted while in office.

Those who think a president can be indicted have cited a 1997 Supreme Court ruling that held that a lawsuit against Mr. Clinton could proceed while he was in office, notwithstanding the burdens that it imposed upon him. They have also pointed to the 25th Amendment, which allows a president who is disabled from performing his duties be temporarily replaced by the vice president.

But Mr. Mueller appears to have far less latitude than either of those predecessors in how he chooses to interpret the law. The regulations that Rod J. Rosenstein, the deputy attorney general, cited when appointing Mr. Mueller say that he must obey the Justice Department’s “rules, regulations, procedures, practices and policies,” and Office of Legal Counsel interpretations of the law are generally binding on the department.