CHICAGO — Attorney General William P. Barr pushed back on Monday on criticism that the Justice Department is investigating the origins of the Russia inquiry to help President Trump settle personal legal and political scores, insisting that he does not serve as the president’s personal lawyer.

“That’s completely wrong and there is no basis for it,” Mr. Barr said in an interview with Fox News on the sidelines of a major law enforcement conference in Chicago. “I act on behalf of the United States.”

Mr. Barr also sought to distance himself from the investigation, though he is closely supervising it. Mr. Barr played down his overseas travel, which has gained attention in recent weeks, as an attempt to open doors for the lead investigator, the veteran prosecutor John H. Durham.

“He is in charge of the investigation,” Mr. Barr said of Mr. Durham. “I’m not doing the investigation.”

Mr. Barr’s comments were his first public remarks after a cascade of revelations about the investigation, including that it has shifted from an administrative review to a criminal inquiry, meaning Mr. Durham can seek court orders for witness testimony and documents and convene a grand jury.

Mr. Trump and his allies have long sought to undermine the origins of the Russia investigation, and depending on what Mr. Durham uncovers and when his findings are made public, his inquiry could provide a boon to Mr. Trump as he seeks re-election. The president has praised Mr. Barr for opening the investigation.

“Thank you, Bill. You’re doing a great job,” Mr. Trump said to Mr. Barr on Monday during a speech at the International Association of Chiefs of Police conference in Chicago. Mr. Trump asked the audience to applaud the attorney general to combat criticism of his work published by “the fake news.”

Mr. Barr traveled to Chicago to attend Mr. Trump’s speech, meet with local law enforcement agencies and visit federal prosecutors.

Mr. Barr’s requests for help from foreign governments for the Durham investigation, including a pair of trips to Rome to meet with Italian intelligence officials, have drawn scrutiny because conservative allies of Mr. Trump have seized on those countries’ roles in the start of the Russia investigation to stoke conspiracy theories.

Mr. Barr portrayed his requests as an effort to aid Mr. Durham. The attorney general said that foreign governments had asked about the scope and nature of the Durham investigation and how the Justice Department would handle confidential information. He said he fielded those questions to help Mr. Durham, not to manage his investigation.

“I initially discussed these matters with those countries and introduced them to John Durham and established a channel by which Mr. Durham can obtain assistance from those countries,” Mr. Barr said, emphasizing that Mr. Durham was running his own investigation.

Mr. Durham, the United States attorney in Connecticut and a veteran of politically charged investigations, and his investigators have interviewed nearly 30 former and current F.B.I. and intelligence officials. They have asked whether any of the officials who investigated Russia’s 2016 election interference and possible links to the Trump campaign exhibited anti-Trump bias.

The Durham team has homed in on aspects of the Russia investigation that Mr. Trump and his allies have long attacked, including the decisions surrounding a secret application to wiretap Carter Page, a Trump campaign adviser who was suspected of being groomed to be a Russian asset. Mr. Page has denied those allegations.

To conduct a thorough review of an investigation, however, Mr. Durham would have to run down all leads, even those that earlier investigations dismissed.

Mr. Barr defended the Durham investigation as “thorough and fair,” adding that Mr. Durham was “making great progress” but declining to detail it.

He also extolled the F.B.I. director, Christopher A. Wray, and the F.B.I. agents whom Mr. Durham has interviewed, for their “outstanding support and responsiveness.” The praise was a sign that Mr. Barr was trying to maintain a good relationship with the F.B.I. even as the Justice Department scrutinizes its most politically consequential investigation in a generation.

Mr. Barr also implicitly criticized Mr. Wray’s predecessor, James B. Comey, whom the president fired in 2017. Mr. Comey led the F.B.I. during the political firestorm of 2016 that consisted not only of the Russia investigation but also of the inquiry into whether Hillary Clinton mishandled classified information by using a private email server.

“I’ve said previously that I felt there was a failure of leadership at the bureau in 2016 and part of 2017, but since Director Wray and his team have taken over there’s been a world of change,” Mr. Barr said. “I think that he is restoring the steady professionalism that’s been a hallmark of the F.B.I.”

Mr. Barr was referring to remarks he made soon after he was confirmed early this year as attorney general when he said that he believed that officials had been “spying” on Mr. Trump’s campaign. The attorney general also raised questions about whether the Russia investigation was “lawfully predicated.”

Shortly after, Mr. Barr opened a limited review of the decisions that led to the opening of the counterintelligence investigation into the Trump campaign — work that eventually morphed into the investigation led by the special counsel, Robert S. Mueller III.

Mr. Mueller found that Russia did interfere in the 2016 election, that it supported Mr. Trump and that the Trump campaign welcomed the help. But he did not find enough evidence to charge anyone from the campaign with conspiring with Russia.