Donald Trump called Scott Morrison to ask for help in an investigation aimed at discrediting the Mueller inquiry, and Morrison agreed to assist.

The call, first reported by the New York Times but confirmed by the Australian government, happened shortly before the Australian prime minister flew to the US to visit Trump last week. White House sources also confirmed the report, the Australian ABC reported.

According to two officials with knowledge of the call, Trump asked Morrison to help the US attorney general, William Barr, find evidence for a review into the Mueller inquiry.

The White House restricted access to the call’s transcript to a small group of the president’s aides, echoing a strategy used to conceal Trump’s July phone call with the Ukrainian president, the Times reported.

“The Australian government has always been ready to assist and cooperate with efforts that help shed further light on the matters under investigation,” the Australian government said in a statement. “The PM confirmed this readiness once again in conversation with the president.”

The dialogue between the Trump administration and the Morrison government has apparently been playing out for some months. On 25 May Trump blasted Australia before leaving on a trip to Japan, declaring he wanted Australia’s role in setting off the FBI inquiry into links between Russia and his election campaign examined by Barr. Trump said he hoped Barr would “look at the UK 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.”

Australia’s foreign affairs minister, Marise Payne, signalled the government was prepared to contribute to the Barr investigation. Payne said at the time Australia had not yet been asked but “we would, of course, consider such a request were it to be made”.

After Trump’s spray, Australia’s ambassador to the US, Joe Hockey, wrote to Barr, copying in the White House chief of staff, Mick Mulvaney. In a letter released on Tuesday, Hockey said: “The Australian government will use its best endeavours to support your efforts in this matter.

“While Australia’s former high commissioner to the United Kingdom, the Hon Alexander Downer, is no longer employed by the government, we stand ready to provide you with all the relevant information to support your inquiries.”

The Mueller inquiry looked at whether Trump worked with Russia to interfere in the 2016 election and delivered its report in April this year, but Mueller testified to Congress in July that its implications continued into the future.

The Mueller investigation began after Australia’s former foreign affairs minister, Downer, was allegedly told about the interference by George Papadopoulos, a Trump campaign aide. Downer then informed the FBI.

​According to Downer, Papadopoulos told him during “a night of heavy drinking”​ in May 2016 ​that Russia had obtained damaging information about Hillary Clinton from her emails.

The US president has described Barr’s review as “investigating the investigators”, and has accused former FBI officials of “treason”.

In May Payne told ABC Radio: “We don’t intend to engage in a public commentary that might entail any risk that we’re seen to prejudice the ongoing examination of these matters in the US.”

On Tuesday, Downer happened to be a guest on ABC’s Radio National breakfast program, discussing China, when the story broke. “I had no idea until this moment you were going to talk to me about this,” he said.

“I’ve got nothing to say about it beyond what I’ve ever said. I don’t know anything at all about conversations that Scott Morrison has had with Donald Trump. These days it’s not something I am privy to.

“I had a conversation with this guy [Papadopoulos], I passed on one element of the convo to the Americans. There is nothing more to it.”

Papadopoulos has denied Downer’s account of events. He welcomed the news that Australia would cooperate with the US.

“Bye, bye Downer,” he wrote on Twitter.

A spokeswoman for Labor’s foreign affairs spokeswoman, Penny Wong, said the prime minister needed to explain his actions. “It is being alleged that president Trump asked Scott Morrison for help in dealing with his political opponents.

“Scott Morrison must immediately come clean on what was discussed. Australians will wonder if any of the treatment he received from the US administration is related to these allegations.”