A Justice Department official told Fox News on Monday that Attorney General Bill Barr asked President Trump to make introductions to foreign countries that might have had information pertinent to U.S. Attorney John Durham's ongoing probe into possible misconduct by the intelligence community at the outset of the Russia investigation.

But, a person familiar with the situation told Fox News it would be wrong to say Trump "pressed" the Australian prime minister for information that could have discredited former Special Counsel Mueller's now-completed probe, as The New York Times reported earlier Monday.

"The countries have been helpful," the source said. "There was no pressing required."

TRUMP DEMANDS SCHIFF RESIGN OVER 'PARODY' READING OF UKRAINE CALL

The president mentioned to reporters publicly on May 24 that he wanted Barr to "look at" a variety of countries.

"But, for over a year, people have asked me to declassify," Trump said. "So, what I’ve done is, I’ve declassified everything. He can look, and I hope he looks at the U.K., and I hope he looks at Australia, and I hope he looks at Ukraine. I hope he looks at everything because there was a hoax that was perpetrated on our country. It’s the greatest hoax."

In response to that public comment, the Australians proactively contracted Barr offering assistance. Fox News has obtained a letter showing Australia's outreach, including an offer to use its "best endeavors" in "support" of Barr's probe.

A senior Australian diplomat told Fox News: "After the president said what he said - we initiated the contact. There was no pressure -- we acted in order to help."

In issuing his directive, the president was letting the heads of other countries know that the attorney general would be contacting the appropriate law enforcement entities in each country, according to the DOJ official. When Barr was in Italy last week, he did talk to law enforcement officials there about Durham's review, Fox News was told.

The DOJ official also stressed that this has been a routine procedure in diplomacy and that Barr would not usually reach out to his direct counterpart in another country unilaterally. Instead, usually there would be an introduction of sorts made at the head-of-state level.

Barr assigned Durham, the U.S. attorney in Connecticut, back in May to conduct the inquiry into alleged misconduct and improper surveillance of the Trump campaign in 2016, as well as whether Democrats were the ones who'd improperly colluded with foreign actors.

"Mr. Durham is gathering information from numerous sources, including a number of foreign countries. At Attorney General Barr’s request, the president has contacted other countries to ask them to introduce the attorney general and Mr. Durham to appropriate officials," Justice Department spokeswoman Kerri Kupec said.

Durham, known as a "hard-charging, bulldog" prosecutor, according to a source, has been focusing on the period before Nov. 7, 2016 — including the use and assignments of FBI informants, as well as alleged improper issuance of Foreign Intelligence Surveillance Act (FISA) warrants. Durham was asked to help Barr to "ensure that intelligence collection activities by the U.S. government related to the Trump 2016 presidential campaign were lawful and appropriate."

Democrats increasingly have targeted Barr. House Speaker Nancy Pelosi, D-Calif., said Friday that Barr has "gone rogue," alleging an attempted "cover-up" of the whistleblower complaint that has led to an impeachment inquiry of the president.

CLICK HERE FOR THE ALL-NEW FOXBUSINESS.COM

Pelosi made the comments on MSNBC's "Morning Joe" after host Joe Scarborough asked if she was concerned that the country's institutions could fail due to Barr's behavior.

"I think where they are going is the cover-up of the cover-up, and that's very really sad for them. To have a Justice Department go so rogue, they have been for a while, and now it just makes matters worse," said Pelosi, faulting Barr for instructing the director of national intelligence to bring the whistleblower complaint to the White House.

Fox News' Bret Baier contributed to this report.