The president’s call came two weeks after he publicly expressed frustration with the Justice Department for failing to give Republican lawmakers documents they are seeking about the basis and findings of the special counsel investigation into whether the Trump campaign worked with the Russians to sway the 2016 election. The president said then that “at some point, I will have no choice but to use the powers granted to the Presidency and get involved!”

That point appeared to be Sunday, close to the first anniversary of the opening of the special counsel investigation, at a time when the president’s frustration about it has reached a fever pitch and he and his allies have ratcheted up their efforts to undercut its credibility. It came as Rudolph W. Giuliani, his private lawyer, said that the special counsel, Robert S. Mueller III, planned to complete by Sept. 1 his inquiry into whether the president had obstructed justice — an apparent attempt by Mr. Giuliani to publicly pressure the special counsel amid negotiations over whether Mr. Trump will be interviewed in the case.

While most presidents who have faced investigations have responded with increased discretion to avoid being seen as trying to influence the outcome, Mr. Trump has dispensed with any notion that he is not trying to do so. He and his aides have branded the investigation a witch hunt and a hoax, called for an end to it, and tried to set its boundaries, and now the president has ordered a review of how it was handled.

“I can’t think of a prior example of a sitting president ordering the Justice Department to conduct an investigation like this one,” said Stephen I. Vladeck, a professor at the University of Texas School of Law. “That’s little more than a transparent effort to undermine an ongoing investigation.”

If Mr. Trump were to follow through with the demand, Mr. Vladeck added, “it seems to me that the recipients of such an order should resign — and that we’re heading for another Saturday Night Massacre.”

Mr. Trump’s directive prompted speculation that he might be trying to push Mr. Rosenstein out of his job without explicitly firing him, a move the president has frequently considered. Mr. Rosenstein pushed back this month against Republican demands for more visibility into the special counsel’s inquiry, saying his department “is not going to be extorted.”

“This demand puts DAG Rod Rosenstein in a difficult position,” Barbara L. McQuade, a former United States attorney in Michigan, said in a post on Twitter. “He can’t open an investigation based on a political demand, but if he refuses and is fired or resigns, he loses control of the Mueller investigation. Maybe just what Trump wants.”