Australia’s ambassador in Washington has flatly rejected a description by the Senate judiciary committee chairman, Lindsey Graham, of Alexander Downer’s role in relaying information to US authorities about Russia obtaining damaging information about Hillary Clinton.

Graham, an influential Republican senator, wrote to the prime ministers of Australia, Italy and the UK calling for their continued cooperation with the US attorney general William Barr’s investigation – a controversial probe established by Donald Trump aimed at discrediting the Mueller inquiry.

In his letter Graham referred to US law enforcement and intelligence communities “accepting information from an Australian diplomat who was also directed to contact [George] Papadopoulos and relay information obtained from Papadopoulos regarding the campaign to the Federal Bureau of Investigation”.

The Mueller investigation began after Australia’s former foreign affairs minister, Downer, was allegedly told about the interference by Papadopoulos, a Trump campaign aide. Downer then informed US authorities. ​According to Downer, Papadopoulos had told him during “a night of heavy drinking”​ in May 2016 ​that Russia had obtained damaging information about Clinton from her emails.

Trump, who is under increasing domestic pressure as prominent Democrats step up calls for his impeachment, has set up the politically charged Barr inquiry as an investigation into the investigators.

Australia’s ambassador, Joe Hockey, told Graham in a response posted on social media on Thursday night that Australia was cooperating with the Barr investigation, and he said Scott Morrison’s government had given a public commitment to assist the inquiry.

But he took issue with Graham’s description of Downer’s activities. “We reject your characterisation of his role,” the ambassador said. “As you have requested, we will work closely with the attorney-general to resolve any misunderstandings in this matter.”

Australia’s response to Senator Lindsey Graham pic.twitter.com/xiQJ26errM — Joe Hockey (@JoeHockey) October 3, 2019

Morrison has been on the defensive about Australia’s participation in the Barr inquiry – a highly partisan exercise – since the New York Times revealed this week that Trump had called the Australian prime minister asking for cooperation in the lead-up to Morrison’s trip to the US last week.

After the Times revealed the call had taken place, Morrison’s office confirmed it had occurred. “The Australian government has always been ready to assist and cooperate with efforts that help shed further light on the matters under investigation,” it said. “The PM confirmed this readiness once again in conversation with the president.”

The dialogue between the Trump administration and the Morrison government over participation in the probe 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 that 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, 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.”

In an interview with Sky News on Wednesday, Morrison argued it would have been “quite extraordinary” not to cooperate with the US president’s request for assistance as he sought to downplay the private phone call that has thrust Australia into the centre of a highly political investigation into the FBI’s inquiry of alleged Russian meddling in the 2016 election.

He did not rule out providing diplomatic cables to the Barr probe sent by Downer as high commissioner to the UK, but said it would be a very “unusual” thing for Australia to do. “Australia would never do anything that prejudices our national interest,” the prime minister said. “That would be very unusual, that would be very uncommon.”

Morrison argued there had been nothing untoward in Downer’s decision to report the Papadopoulos meeting, saying it was not an issue that he had needed to pay any attention to while prime minister and it was not the subject of any Australian investigation.

“Australia’s conduct here is not in question,” Morrison said. “I wasn’t there, it was some time ago, there is nothing to suggest that has been put in the public domain that there is any matter for Alexander Downer to address, nor am I aware of anyone suggesting any inappropriate behaviour by him.”

Guardian Australia revealed this week that Downer had taken the then prime minister, Malcolm Turnbull, and senior colleagues by surprise when he relayed information to the US chargé d’affaires in London in July 2016 about his now infamous conversation with Papadopoulos.

The conversation was recorded in a diplomatic cable back to Canberra. But the first senior players in Canberra knew of Downer’s conversation with America’s top diplomat in London was when the Australian government was contacted by the FBI for more information. That diplomat-to-diplomat conversation, sources insist, was unauthorised.