A bid to refer Scott Morrison to a powerful parliamentary committee over his secret appointments to five ministries has been refused.
Speaker Milton Dick has written to Greens leader Adam Bandt advising there wasn't enough evidence to refer Mr Morrison to the privileges committee on the grounds he misled parliament.
In the letter, Mr Dick sets out the three tests that need to be met.
They include the need to establish the statement had been misleading, the parliamentarian knew it was incorrect, and they had acted deliberately.
It comes as former senior Liberals backed Anthony Albanese's decision to push ahead with an inquiry into Scott Morrison's secret ministries.
The prime minister is expected within days to announce the name of an eminent legal figure to head up an inquiry into Mr Morrison's decision to appoint himself to five ministries and keep most of them secret from his fellow cabinet members.
Mr Albanese on Tuesday released advice from the solicitor-general which found Mr Morrison did not break any laws in holding the resources portfolio.
But the solicitor-general said taking on the portfolios was at odds with the principle of "responsible government".
Former prime minister Malcolm Turnbull said the inquiry needed to go beyond the conduct of Mr Morrison and examine the prime minister's department and the governor-general's office.
"I remain astonished that there was apparently no pushback to Morrison when he embarked on his bizarre secret accumulation of power," he said on Twitter.
"How did all these experienced people allow Morrison to do this? If any of them had dug their heels in, pushed back, and done so in writing it is hard to believe even the self described bulldozer would have persisted."
Former Liberal foreign minister Julie Bishop said she understood why the government had announced an inquiry.
"The solicitor-general's advice does raise a number of questions that I believe should be examined," she told Nine on Wednesday.
"It will have to be a non-political inquiry. It can't be headed up by, for example, the head of prime minister and cabinet because presumably what the departmental offices knew would also be the subject of the inquiry."
However, Liberal frontbencher Stuart Robert said comments such as that from Deputy Prime Minister Richard Marles, who said Mr Morrison should face "severe consequences" over the controversy, showed there were ulterior motives.
"Mr Marles' comments sounds like a political witch hunt," he told ABC Radio on Wednesday.
"You start to wonder what the government's intent is."
Former prime minister Tony Abbott has described Mr Morrison's conduct as "highly unconventional, highly unorthodox and shouldn't have happened".
University of Sydney constitutional law professor Anne Twomey said it would be "inappropriate" for the communications between the governor-general and the prime minister to be revealed.
"Those matters are confidential, there are good reasons to maintain that relationship of confidentiality," she said.
According to the solicitor-general advice, the governor-general is required to act upon advice, but always has the right to "be consulted, to encourage and to warn in respect of ministerial advice".
Attorney-General Mark Dreyfus said the solicitor-general's advice was "deeply alarming", reinforcing the need for an inquiry.
"We're going to have an inquiry, we're just now working out the details of that inquiry so that we can look into exactly what happened, and then get some recommendations to make sure that it never happens again," he told the Nine Network.
Mr Morrison has indicated he would take part in an inquiry if it was a "process to learn lessons from the pandemic" and involved scrutiny of the states and territories.
Mr Dreyfus said the comments weren't surprising.
"Of course (Mr Morrison) wants it to be broader, and of course, he wants to hide behind the pandemic," he said.
