When Senate Democrats asked Mr. Barr in a budget hearing this month whether Mr. Mueller was indeed leading what Mr. Trump has called a “witch hunt,” Mr. Barr demurred. “If you are somebody who’s being falsely accused of something, you would tend to view the investigation as a witch hunt,” he said.

“What Barr did was try to take advantage of knowing that Mueller was playing things square and by the book,” said Joyce Vance, a former United States attorney in Alabama. “Mueller did things the right way, and there is undoubtedly a cost for that.”

Ms. Vance said that during the Watergate investigation, younger prosecutors on the team were encouraged to give interviews to help engender the public’s faith in the inquiry. Mr. Mueller was strict about his prosecutors not speaking, his lawyers careful not to say anything about the investigation when approached by reporters.

Mr. Mueller’s instincts were a departure from those of Ken Starr, the independent counsel who investigated President Bill Clinton. Mr. Starr gave interviews and speeches while prosecuting the case, once holding an impromptu news conference in his front yard to defend the scope and speed of his investigation and compare himself to Sgt. Joe Friday from the television series “Dragnet.”

Mr. Mueller stayed silent, growing into an almost mythological figure in Washington, as a public hungry for clues about his investigation scrutinized his body language and documented chance sightings. Photographers gathered last week outside a restaurant he frequented during the investigation. His patronage recently revealed, he never showed.

The report itself — dense in both language and layout — reflected Mr. Mueller’s caution and stood in contrast to Mr. Starr’s more conversational and discursive style. The section on episodes of possible obstruction unfolds in devastating chronological detail but avoids commenting on the powerful political context.

“Lofty prose is not his thing,” said Glenn Kirschner, who worked for Mr. Mueller in the homicide unit of the United States attorney’s office in Washington. “It’s going to be almost terse.”