U.S. President Donald Trump pushed the Australian prime minister during a recent telephone call to help Attorney General William P. Barr gather information for a Justice Department inquiry that Mr. Trump hopes will discredit the Mueller investigation, according to two American officials with knowledge of the call.

The White House curbed access to a transcript of the call – which the president made at Mr. Barr's request – to a small group of aides, one of the officials said. The restriction was unusual and similar to the handling of a July call with the Ukrainian president that is at the heart of House Democrats' impeachment inquiry, according to The New York Times.

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Like that call, Mr. Trump's discussion with Prime Minister Scott Morrison of Australia shows the president using high-level diplomacy to advance his personal political interests.

The discussion with Mr. Morrison shows the extent to which Mr. Trump views the attorney general as a crucial partner: The president is using federal law enforcement powers to aid his political prospects, settle scores with his perceived "deep state" enemies and show that the Mueller investigation had corrupt, partisan origins.

The Justice Department inquiry and a parallel but unconnected effort by the president's personal lawyer Rudolph W. Giuliani represent a kind of two-front war. Mr. Trump has said that Mr. Barr can help him validate his 2016 electoral victory, and Mr. Giuliani has been trying to unearth damaging information about former Vice President Joseph R. Biden Jr. in anticipation of the 2020 race.

As part of his efforts, Mr. Barr in recent months has asked the president to facilitate communications with foreign officials and has made at least one trip to Italy to secure cooperation, according to a department official. The inquiry is examining American intelligence and law enforcement activity around the Trump campaign and whether it was legal.

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Mr. Trump initiated the discussion with Mr. Morrison in recent weeks explicitly for the purpose of requesting Australia's help in the review, according to the two people with knowledge of the discussion.

In making the request – one of many at Mr. Barr's behest – Mr. Trump was in effect asking the Australian government to investigate itself. F.B.I. investigators began examining Trump ties to Russia's 2016 election interference after Australian officials reported that Russian intermediaries had made overtures to Trump advisers about releasing information that would damage Hillary Clinton's campaign.

Australia's top diplomat in Britain had met in London in May 2016 with George Papadopoulos, a Trump campaign foreign policy adviser who revealed the Russian offer of dirt on Mrs. Clinton.

Mr. Papadopoulos also said that he had heard from an academic named Joseph Mifsud that the Russians had "thousands" of Mrs. Clinton's emails. Mr. Mifsud, who was last seen working as a visiting professor in Rome, has disappeared. Trump allies including Mr. Giuliani have put forth an unsubstantiated claim that Western intelligence agencies planted Mr. Mifsud to trap Mr. Papadopoulos.

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Mr. Barr met with Italian government officials on Friday in Italy. A Justice Department spokeswoman, Kerri Kupec, would not say whether he discussed the election inquiry or Mr. Mifsud.

"At Attorney General Barr's request, the president has contacted other countries," Ms. Kupec said, to ask for introductions to foreign officials for the Justice Department inquiry, which is being led by John H. Durham, the United States attorney in Connecticut.

As he did with Mr. Morrison, Mr. Trump told the officials that the Justice Department planned to contact their law enforcement agencies, a Justice Department official said.

In a statement, Hogan Gidley, a White House spokesman, sought to focus on Mr. Trump's political opponents. "The Democrats clearly don't want the truth to come out anymore as it might hurt them politically, but this call relates to a D.O.J. inquiry publicly announced months ago to uncover exactly what happened," Mr. Gidley said.

On Monday evening, a spokesman for Mr. Morrison said that "the Australian government has always been ready to assist and cooperate with efforts that help shed further light on the matters under investigation."

"The P.M. confirmed this readiness once again in conversation with the president," he added.