The president’s strategy is being directed by Pat Cipollone, the White House counsel, and senior Justice Department officials. Like Attorney General William P. Barr, Mr. Cipollone has strong views about executive power.

Mr. Trump has been watching Fox News and other coverage of congressional efforts to obtain the parts of Mr. Mueller’s report that were redacted by Mr. Barr, people close to him said. At times, his impulses have contradicted the lawyers’ advice, they said.

He has asked some confidants why they should not just reveal everything in the 448-page Mueller report, the vast majority of which has already been made public. But he has also said he wants everyone to move on so he can concentrate on a presidential agenda, a sentiment he expressed on Twitter throughout last weekend.

As for whether Mr. Mueller should be allowed to testify before the House Judiciary Committee, the president reversed himself on Thursday and said that he would leave the decision to Mr. Barr, who has said he does not object to such an appearance. But in private, Mr. Trump has continued to poll-test advisers about whether the Justice Department should instead seek to block Mr. Mueller from appearing.

Legal scholars disagree about the administration’s chances of prevailing in court on its privilege claim and subpoena fights, but the White House sees little downside in waging the battle. Even if Mr. Trump were to lose, the more that the various investigations of the president look like a partisan food fight, the easier it may be to dismiss them as mere politics.

Yet the president risks actually pushing Democrats into doing what they otherwise might not have. After Mr. Mueller wrapped up his investigation by saying that he had not established a conspiracy between Mr. Trump and Russia and could neither accuse nor exonerate him of obstructing justice, House leaders poured water on the prospect of impeachment. While Democrats could impeach him in the House, there is no sign that they could muster 20 Republican senators needed for the two-thirds vote required for conviction in the Senate.