WASHINGTON — Attorney General William P. Barr distanced himself again from President Trump on Monday, saying he saw no reason to appoint special counsels to oversee the Justice Department’s criminal investigation into Hunter Biden, son of President-elect Joseph R. Biden Jr., or to investigate Mr. Trump’s baseless claims of widespread voter fraud.

At a news conference to announce charges in an unrelated terrorism case, Mr. Barr, who is stepping down in two days, said that he did not “see any reason to appoint a special counsel” to oversee the tax investigation into the younger Mr. Biden.

“I have no plan to do so before I leave,” Mr. Barr said. “To the extent that there is an investigation, I think that it’s being handled responsibly and professionally.”

He also said that he would name a special counsel to oversee an inquiry into election fraud if he felt one were warranted. “But I haven’t, and I’m not going to,” Mr. Barr said.

After Mr. Trump’s loss to Mr. Biden, the president and his allies have seized on conspiracy theories about election fraud and considered legally questionable actions to cast doubt on the validity of the outcome or even seek to overturn it. Mr. Barr’s statements, in his final days on the job, seemed to signal that there was no appetite at the Justice Department to be drawn into any such efforts.

But it is unclear how much pressure Mr. Trump might put on Mr. Barr’s replacement, Jeffrey A. Rosen, the current deputy attorney general, who will lead the department on an acting basis for the remaining weeks of the president’s term and whose approach to dealing with Mr. Trump is unknown.

At a minimum, Mr. Barr’s statements on Monday give Mr. Rosen cover not to appoint special counsels to look into voter fraud or Hunter Biden, and would make the optics of any decision to go ahead with such appointments more difficult for both Mr. Rosen and Mr. Trump.

Mr. Rosen has not signaled his specific intentions. But he has held discussions about the ramifications of appointing a special counsel to oversee the investigation into Hunter Biden, according to a person familiar with those conversations who is not authorized to publicly discuss them.

He said in an interview with Reuters last week that he would make decisions on all issues, including the potential appointment of a special counsel, “on the basis of the law and the facts.”

Mr. Barr’s comments are certain to further poison his relationship with Mr. Trump, who believes that the attorney general should have more forcefully used the Justice Department to attack Mr. Biden and his family in the weeks before the election and to cast doubt on the results after the votes were cast.

Long been regarded as Mr. Trump’s most loyal and effective cabinet member, Mr. Barr, a believer in strong presidential power, brought the Justice Department closer to the White House than any attorney general since John Mitchell, who ran President Richard M. Nixon’s re-election campaign and was deeply involved in Watergate.

Mr. Barr’s handling of the special counsel’s investigation into the intersection of Russia and Mr. Trump’s 2016 campaign amounted to a gift to the president. He presented it in the best possible light for Mr. Trump before its public release and ultimately concluded that the president had not obstructed justice, despite his efforts to shut down the inquiry.

The Justice Department’s independent inspector general found that the senior officials at the bureau had sufficient reason to open the investigation. A judge later called Mr. Barr’s summary of the report by the special counsel, Robert S. Mueller III, misleading.

Convinced that the F.B.I. had overstepped its authority in investigating the Trump campaign, Mr. Barr asked a federal prosecutor, John H. Durham, to look into the origins of the Russia investigation. In October, the attorney general appointed him to be a special counsel with a mandate to continue exploring whether the inquiry was wrongfully opened.

Mr. Barr broke with longstanding norms when he spent the months leading up to the election echoing Mr. Trump’s unsubstantiated claims that mail-in ballots would result in widespread voter fraud. In strikingly political remarks for an attorney general, he later said the country would be “irrevocably committed to the socialist path” if the president were not re-elected.

He also approved the withdrawal of criminal charges against Michael T. Flynn, the president’s first national security adviser, and overruled prosecutors who requested a long sentencing recommendation for Roger J. Stone Jr., one of Mr. Trump’s longtime advisers.

But his relationship with the president fractured after the election after he said in an interview this month that he had not seen voter fraud “on a scale that could have effected a different outcome in the election.”

Tensions between them escalated after it became clear that Mr. Barr had kept the investigation in Mr. Biden’s son under wraps during the presidential race. While it is department policy not to discuss investigations that could affect the outcome of an election, Mr. Trump accused his attorney general of disloyalty for not publicly disclosing the matter during the campaign.

With the president growing more furious and his allies constantly attacking Mr. Barr on social media and cable news for his perceived disloyalty, the president said last week that Mr. Barr would depart on Wednesday.

Mr. Trump’s efforts to overturn the election have grown more frantic since he announced that Mr. Barr would step down. On Friday, he discussed with aides in the Oval Office about naming Sidney Powell to be a special counsel overseeing a voter fraud inquiry. Ms. Powell, who worked as a lawyer for his campaign, has promoted unfounded conspiracy theories that Venezuela rigged the presidential election using doctored voting machines.

Ms. Powell met briefly with Mr. Trump on Monday, a person briefed on their discussion said. Separately, the president met with a group of House Republicans, including Representative Mo Brooks of Alabama, who is pushing a congressional challenge of electoral votes from a half-dozen battleground states that were won by President-elect Joseph R. Biden Jr.

Mr. Brooks said that he and “people with firsthand knowledge of voter fraud” met over the course of several hours with Mr. Trump and others. “All in all, our effort to object to states that have such flawed election systems as to render them untrustworthy is full speed ahead,” Mr. Brooks said.

The president has raised the possibility of an executive order to have the Department of Homeland Security seize and examine voting machines for evidence of tampering. His personal lawyer, Rudolph W. Giuliani, has also sought to have the department seize the machines, an idea rejected by homeland security officials.

On Monday, Mr. Barr said he saw “no basis now for seizing machines by the federal government.”

White House lawyers have told Mr. Trump that he does not have the authority to take these actions, but his allies have pushed the president not to heed their advice.

Now Mr. Rosen will have to contend with the possibility that Mr. Trump will run a parallel pressure campaign on the Justice Department.

Mr. Rosen, a longtime corporate lawyer with no experience as a prosecutor, had never worked at the Justice Department before he became Mr. Barr’s top deputy in May 2019. His previous government service includes a stint as general counsel of the Transportation Department and of the White House’s Office of Management and Budget under George W. Bush, as well as as the No. 2 official of the Transportation Department under Mr. Trump.

The question of how far an attorney general can and should go to further Mr. Trump’s political agenda has defined the tenures of both Mr. Barr and his most recent predecessor, Jeff Sessions. But Mr. Rosen will be stepping into the role at a time when the question is as intense as it has ever been.

Unlike Mr. Barr and Mr. Sessions, Mr. Rosen does not have a long relationship with the department and no one is sure how much he is inclined to be a check on the president and protect the long-term interests of the department.

Mr. Rosen worked largely in Mr. Barr’s shadow at the department. After Mr. Barr announced that he would leave, Mr. Rosen said that he was “honored at the trust and confidence” that Mr. Trump had placed in him to lead the department and that he would “continue to focus the implementation of the department’s key priorities” and maintain “the rule of law.”

Maggie Haberman contributed reporting from New York.