The US President has effectively embraced the wider conspiracy theory, asking his Attorney-General William Barr to investigate how the Russia probe got started and told reporters that "I hope he looks at Australia" as well as Britain and Ukraine for their involvement.

Mr Downer called it "a complete beat-up" and said the US President likely called an investigation into the origins of the Russia probe because he saw suggestions of a conspiracy in American media.

Mr Downer famously met with Trump campaign staffer George Papadopoulos at a London wine bar in 2016, when Mr Papadopoulos said Russia had indicated to the campaign that it could help by releasing thousands of stolen emails that were damaging to rival Hillary Clinton.

Mr Downer reported the conversation back to Canberra via diplomatic cable. Canberra passed the information on to Washington and it reportedly contributed to the beginning of the FBI probe into potential collusion between the Trump team and Moscow, which then morphed into the inquiry by special counsel Robert Mueller.

Mr Trump swung onto the offensive in the wake of the Mueller report's release and with the request to investigate its origins, he appears to be endorsing a theory - being pushed by Mr Papadopoulos and in conservative US media including Fox News - that some US intelligence and FBI officials conspired with help from foreign partners to concoct the Russia allegations and undermine the Trump campaign and presidency.

Mr Downer, who was Australia's high commissioner to Britain when he met Mr Papadopoulos - who went on to spend 12 days in jail for lying to the FBI - laughed off the theory that he had been sent to spy on the junior campaign aide.

"The FBI and the State Department know that's not true ... As if somebody would ring me up and say, 'Will you go and spy on some clown called Papadopoulos who's a volunteer from the Trump campaign?'

"Are you kidding ... If you wanted to spy on the Trump campaign, wouldn't you spy on a main player ... Steve Bannon or someone like that?"

Mr Downer said Mr Trump likely called the investigation because he'd seen the theory promoted in the media.

"People make these allegations. He sees the allegations and he wonders what that's all about. That's fair enough. I don't think there's any big deal there, particularly as there's nothing to find out," he said.

Mr Trump has claimed exoneration from the Mueller report and even called the probe "an attempted coup", though Democrats and Trump critics say the report has raised troubling issues about the campaign and administration.

Mr Downer avoided directly criticising Mr Trump, saying: "I'm not against him."

Mr Downer said the matter was "to do with American politics" and he was comfortable about that.

"They have to play their politics ... He's obviously very good at politics because he became the President."

He added: "The more it's investigated, the more it'll be shown to be a complete beat-up. So they're welcome to investigate. I don't care."

He dismissed suggestions that the Barr investigation could smear Australia either way, saying it could be "handled with consummate ease" by the Morrison government.

Michael Fullilove, executive director of the Lowy Institute, said even accounting for Mr Trump's history of scepticism about traditional US alliances, it was "disturbing to see him try to drag the UK and Australia into America's fevered conspiracy politics".

"Australia is the United States' most reliable ally," he said. "We don't interfere in American elections and we don't deserve to be treated like this."