Under the regulation, if Mr. Whitaker were to block any of Mr. Mueller’s steps, Congress must be notified.

Mr. Trump was “clearly” motivated to replace Mr. Sessions to affect the Mueller investigation, said David Kris, a founder of the Culper Partners consulting firm who led the Justice Department’s national security division during the Obama administration.

An open question, he said, is what Mr. Whitaker will do — and what reactions that will provoke from Mr. Mueller, other federal prosecutors and House Democrats.

“What guerrilla-war tactics will he try to take to limit Mueller’s activities?” Mr. Kris said of Mr. Whitaker. “Under the regulation, he has a bunch of supervisory actions he can take and if he does undertake those actions, the more extreme they are, the more likely they will provoke reactions from other players in this drama.”

Can Mr. Whitaker fire Mr. Mueller?

The regulation that Mr. Rosenstein invoked when appointing Mr. Mueller also made it more difficult to fire him. It said that the attorney general may remove the special counsel only for cause, like misconduct of some kind, rather than at will.

Mr. Whitaker could decide that Mr. Mueller has committed misconduct and fire him, or he could revoke the protections that the regulation provides to Mr. Mueller and then fire him without cause.

Can Mr. Whitaker quash a Mueller report?

When Mr. Mueller completes his work, he is to deliver a report about his findings to the attorney general, according to the regulation. It would then be up to the attorney general — now Mr. Whitaker — to decide whether to turn that document over to Congress or keep it secret.