For insight on what he will do next, those who have known him for years say, do not look at the mythology that has built up since Mr. Mueller was appointed 15 months ago. Look instead to his four decades of government service.

As he advanced from line prosecutor to top Justice Department official to head of the F.B.I., his time was marked by aggressive prosecutions but also a deference at key moments to precedent, tradition and higher office. “He’s the last guy who’s going to do anything that’s even slightly a departure from the bedrock principles,” said Glenn Kirschner, who worked alongside Mr. Mueller as a homicide prosecutor.

The special counsel investigation has followed a familiar path, colleagues said, largely because Mr. Mueller, a publicity-averse 74-year-old who is as conservative as his go-to outfit (dark suit, white shirt — never blue — and a button-down collar), has stuck to his approach.