“The PM confirmed this readiness once again in conversation with the President.”
The revelation of the call came just over a week since Mr Morrison appeared at a campaign-style rally alongside Trump in Ohio and dined with him at a state dinner at the White House.
Two administration officials said the call between Mr Trump and Mr Morrison had occurred in recent weeks, and was explicitly made to discuss the Russia issue.
Mr Trump’s interactions with foreign leaders are coming under intense scrutiny following the release of a transcript that showed him pressuring the Ukrainian President to investigate potential 2020 Democratic rival Joe Biden.
The Democrats have launched an impeachment inquiry into Mr Trump, a move polls show is increasingly popular with the American public.
Mr Trump announced in May that he had asked his Attorney-General William Barr to investigate Australia’s role in sparking the 2016 FBI investigation into his campaign’s Russia connections.
“He can look and I hope he looks at the UK and I hope he looks at Australia and I hope he looks at Ukraine,” Mr Trump said at the time.
“I hope he looks at everything, because there was a hoax that was perpetrated on our country.”
Australia’s ambassador to Washington, Joe Hockey, wrote to Barr in May to offer Australia’s help in the investigation.
“I refer to President Trump’s announcement on 24 May that you will investigate the origins of the Federal Bureau of Investigations probe into Russian links to the 2016 elections,” Mr Hockey wrote in the letter, which was made public on Tuesday.
“The Australian Government will use its best endeavours to support your efforts in this matter.”
A Justice Department spokesperson confirmed that Mr Barr had asked Mr Trump to raise the issue with foreign leaders.
“As the Department of Justice has previously announced, a team led by US Attorney John Durham is investigating the origins of the US counterintelligence probe of the Trump 2016 presidential campaign,” the spokesperson said.
“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.”
Australia’s former high commissioner to the United Kingdom, Alexander Downer, helped trigger an initial FBI investigation into Trump’s links with Russia after having drinks in London with Mr Trump’s campaign aide George Papadopoulos.
Mr Downer has said that Mr Papadopoulos told him at the bar Russia had damaging material on Mr Trump’s presidential rival Hillary Clinton.
He forwarded the information on to officials in Canberra, who then passed on to US intelligence services, who had also received warnings from Five Eyes’ intelligence services.
Speaking on Radio National on Tuesday morning, Mr Downer said: “I’ve got nothing to say about it beyond what I’ve ever said … I mean I had a conversation with this guy, I passed on the conversation or that one element of the conversation to the Americans and there’s just nothing more to it.”
Mr Downer said he had no idea what Mr Morrison and Mr Trump had discussed in their phone call.
A series of new polls showed a surge in support for impeachment among the American public.
A poll from Quinnipiac University released on Tuesday showed a 20 per cent swing in favour of impeachment over the past week.
The poll showed 47 per cent of Americans favour impeachment and 47 per cent are opposed, a big turnaround from a 37-57 split against impeachment the week before.
House Democrats on Tuesday issued a subpoena for Trump’s personal lawyer, Rudy Giuliani, to produce communications and other records related to the Ukraine investigation.
Matthew Knott a reporter for The Sydney Morning Herald and The Age based in the United States.