Encounters with reporters have proved more delicate. In one instance, Uzo Asonye, one of the special counsel prosecutors, stepped into an elevator with a colleague whom he stopped midsentence.

“Stop,” he said, gesturing to the reporter’s press badge. He held up his hand to silence her.

He turned to the reporter with a smile. “Sorry. I can’t talk to you.”

The prosecutors’ habits are to be expected in such a big case, former members of independent counsel teams said. The difference this time is the magnitude of the investigation paired with an era of instant news.

“This is unusual,” said Solomon L. Wisenberg, a deputy independent counsel who was selected by Judge Kenneth W. Starr to handle the grand jury questioning of President Bill Clinton. “This is a major, major trial with intense press interest in an era when you have 24-hour cable news.”

During the 2007 trial of I. Lewis Libby Jr., Vice President Dick Cheney’s former chief of staff who was convicted of perjury in connection with the leak of a C.I.A. officer’s identity, the prosecution team took unusual measures to deter attention, said Peter R. Zeidenberg, a deputy special counsel in the case. Patrick J. Fitzgerald, the lead prosecutor, at one point negotiated with a photographer to allow for a picture of him picking up coffee. The deal, Mr. Zeidenberg said, was that the photographer would then leave Mr. Fitzgerald alone.

Perhaps no member of Mr. Mueller’s team has drawn more curiosity than the special counsel himself, who has not spoken publicly about the inquiry. The void has filled with speculation about the smallest observations — even about his choice of watch, the hyper-accurate Casio DW-290, which he wears with the face on the inside of his wrist.

Public sightings of him are scarce. A New York Times reporter spotted Mr. Mueller leaving a 7-Eleven convenience store in Washington on a Saturday morning this winter in a cinched-waist parka and gym clothes, walking to a small sport utility vehicle. Mr. Mueller got behind the wheel, made a U-turn to cross a double yellow line and drove away.