The Prime Minister will today receive legal advice on whether his predecessor Scott Morrison broke any laws by secretly taking on five ministerial roles.
Anthony Albanese has also flagged a separate review of Mr Morrison's conduct, which has been welcomed by Liberal moderate Bridget Archer, who believes her former leader should reflect on his position in parliament.
The federal Greens are also agitating for a broad inquiry that would also consider the role of the Governor-General and the federal public service.
Cabinet minister Brendan O'Connor told the ABC that "an unprecedented contravention of the Westminster system" deserved thorough scrutiny.
"I don't think Mr Morrison has come entirely clean about what motivated him," Mr O'Connor said.
"We are concerned that every time we hear a colleague of Mr Morrison talk about what they know, more and more seems to be revealed."
On Sunday, Mr Albanese said there was no suggestion Mr Morrison had acted unlawfully but that there was clearly "a need for proper scrutiny of what occurred".
"This was an undermining of our parliamentary democracy, and what the Solicitor-General will advise on is of course the legal issues," Mr Albanese told Sky.
Archer: Morrison should reflect on position in parliament
Ms Archer is also calling for further investigation of Mr Morrison's behaviour, arguing Australians deserve more transparency.
"Certainly, I think there needs to be some form of investigation or inquiry around how this occurred," Ms Archer told the ABC.
"The commentary that we have heard in the past few days would indicate that Australians expect the traditional conventions of our parliament and our Westminster systems be upheld."
Ms Archer did not directly call for Mr Morrison to resign from parliament as her colleague and former Home Affairs Minister Karen Andrews has but said he should reflect on his position.
"I do just think that people should reflect on the great privilege and responsibility that they have when they are elected to these roles, and think about whether they are fulfilling those obligations," she said.
"If they are not, then they might want to reflect on doing something else.
"I am not responsible for those actions but I am forced into a situation where I'm meant to defend them and I won't."
Opposition Leader Peter Dutton has described Mr Morrison's actions as "inappropriate", but has also called Mr Albanese's reaction "borderline hysterical".
Mr Morrison said Mr Albanese's response was opportunistic.
"He sees political opportunity and he's taken it – fair enough," Mr Morrison told Sydney radio station 2GB last week.
Ms Archer said she had not decided whether Mr Morrison should be referred to parliament's privileges committee, but said she had "an open mind" on next steps.
"While this may not be corrupt behaviour … and it may not be unlawful behaviour, it certainly doesn't pass the pub test and we want to have actions that we can have trust and confidence in," she told the ABC.
Greens want Governor-General's role investigated
The Prime Minister has defended the conduct of Governor-General David Hurley, who swore Mr Morrison into additional portfolios, saying he was merely acting on the advice of government.
In a statement released last week, General Hurley said he had "no reason" to think Mr Morrison would not announce the new ministerial powers to the public.
But Greens senator David Shoebridge said General Hurley had questions to answer given he approved the Home Affairs, Treasury and Resources portfolio powers many months after the initial appointments.
"If on the first occasion [in 2020] he had seen there had not been any communication about the secret ministry, well maybe that's acceptable," Senator Shoebridge told the ABC.
"But what about the second? The third? The fourth and the fifth?"
Ms Archer said she remained open minded about the structure of an inquiry.
"I don't necessarily see why not [to include the Governor-General and public service]," she said.
Mr O'Connor said the focus of any inquiry should be on the former prime minister, not the Governor-General.
"The convention is the governor-general acts on the advice of the prime minister and therefore the focus, quite rightly, is on the prime minister," Mr O'Connor said.
Mr Shoebridge has also called for the role of the public service to be investigated.
"The Department of Prime Minister and Cabinet seems to have had a significant role in establishing these secret ministries and that too needs to be investigated."