Australian prime minister Scott Morrison is under pressure to reveal the details of Donald Trump’s request for assistance in dealing with the Mueller inquiry.

Mr Morrison confirmed on Tuesday that he agreed to assist Mr Trump in a phone call in May, but opposition frontbencher Bill Shorten called on the prime minister to release the full transcript of the conversation.

Mr Trump's call to Mr Morrison is reported to have contained a request to help the US investigate the origins of the Mueller inquiry into Russian collusion, which the US president has repeatedly framed as a witch hunt.

Records of the phone call are said to have been restricted. The New York Times said that access to the call’s transcript was restricted to a small group of the president’s aides in the same way that Mr Trump's call to the Ukrainian president - that triggered impeachment proceedings in the US - was dealt with.

The Mueller inquiry is said to have been partly sparked by the former Australian high commissioner to the UK, Alexander Downer. Mr Downer allegedly fed information to the Australian government about a Trump aide working with Russian officials to discredit Hilary Clinton. The information was passed to the US.

Mr Trump's personal lawyer has promoted the theory that the source of the information in the UK was planted by Western intelligence agencies.