Democrats have demanded that Mr. Barr protect Mr. Mueller as he completes the investigation into Russia’s interference in the 2016 election, including whether Mr. Trump sought to obstruct the inquiry on behalf of Moscow. Democrats have also focused on whether Mr. Barr would turn over to Congress any report Mr. Mueller compiles .

Senator Lindsey Graham, Republican of South Carolina and the new Judiciary Committee chairman, told reporters after meeting with Mr. Barr last week that the nominee had said he saw no reason to fire Mr. Mueller and had pledged to “err on the side of transparency” about any report. But neither statement addressed what he would do if Mr. Trump ordered him to act otherwise.

Mr. Barr is likely to be confirmed because Republicans control the Senate and because defeating him would leave in place the acting attorney general, Matthew G. Whitaker, a Trump loyalist whose installation in that role Democrats see as illegitimate and a threat to Mr. Mueller. Ethics officials advised Mr. Whitaker to recuse himself from the Russia case, but he refused.

But Mr. Barr has already drawn scrutiny over the revelation last month that he sent an apparently unsolicited 19-page memo to the Trump legal team in June arguing that Mr. Mueller should not be permitted to investigate Mr. Trump for criminal obstruction of justice.

Mr. Barr’s argument derived from his broad view of executive power: The Constitution, he claimed, does not permit Congress to make it a crime for the president to exercise his executive powers corruptly — even if he were to fire a subordinate, pardon someone or use what Mr. Barr termed his “complete authority to start or stop a law enforcement proceeding” to cover up crimes by himself or his associates.

The claim that the framers of the Constitution empowered presidents to impede investigations for corrupt ends goes too far, many legal scholars say. But Supreme Court precedents offer few definitive guideposts, giving the attorney general broad latitude.

“The interpretive approach of Justice Department lawyers to the Constitution is very important because many separation-of-powers issues never wind up in court,” said Peter Shane, an Ohio State University law professor. “Barr’s method is not uniquely his, but it does represent a particularly aggressive school of executive power thought.”