Anthony Albanese has revealed "there may be more" portfolios that former prime minister Scott Morrison secretly appointed himself to, as he launches an investigation into the bombshell revelations.

Describing the situation as "extraordinary" and "unprecedented", the Prime Minister said he simply could not understand the mindset that decided keeping Morrison's extraordinary move a secret was a good idea.

So far, it has emerged that Morrison was appointed as a Minister for Health, Finance and Resources during his time in power through a secret mechanism that did not require him to make the change public. Only then-Health Minister Greg Hunt was aware that Morrison was joining his portfolio.

Cabinet will be briefed on the unfolding scandal this morning, but preliminary advice suggests that the three portfolios that Morrison is believed to have been secretly appointed to may not be the full extent of the changes.

"There may well be more,'' Albanese told ABC Radio National on Tuesday.

"But I'll have more to say about that. It may well be that it takes some time to get to the bottom of this.

"This really does undermine our democracy. Our democracy is precious and it relies upon accountability.

"And this, this cowboy action, I likened it to some tin-pot regime. Well, this is Australia."

Albanese said he was "not aware" whether or not Morrison secured extra pay for his additional jobs, but doubted this was the case.

Solicitor-General Stephen Donaghue QC is also probing the ­legality of Morrison's ministerial arrangements.

Australian Prime Minister Anthony Albanese. Photo / AP

In a statement, Governor-General David Hurley insisted he was acting on the advice of the former prime minister when swearing him into the extra portfolios, and disclosing the arrangements was a matter for him.

Asked if he still had confidence in the Governor-General, Albanese said his job was to take the advice of the prime minister.

"The Governor-General acted on the advice of the government of the day,'' he said.

"Let's be very clear here, it is Scott Morrison that initiated this extraordinary and unprecedented action.

"I think that the blame for this lands fairly and squarely with the former government — not just the prime minister — clearly other ministers knew that this was going on, they chose not to make it public."

On Sunday, news.com.au revealed Morrison had sworn himself in as resources minister without the knowledge of the existing minister, Keith Pitt. He ultimately used that power to roll Pitt on a plan to drill for gas off the New South Wales coast.

Revelations emerged over the weekend via the new book Plagued, that in March of 2020, Morrison was sworn in as a second health minister and second finance minister.

None of these moves were revealed to the public. Former Health Minister Greg Hunt was briefed on the changes but former Finance Minister Mathias Cormann was not.

Morrison broke his silence on the matter on Monday, texting a Sky News journalist to say he doesn't "engage in day-to-day politics".

He was responding to Sky News host Kieran Gilbert, who offered him a right of reply to Albanese, who had blasted Morrison's secrecy.

"Haven't seen what he has said," Morrison texted. "Since leaving the job I haven't engaged in any day-to-day politics."

Albanese said that response was unacceptable.

"Well, he's a member of Parliament,'' he said. "I find that quite an extraordinary dismissal by a former prime minister."

The former prime minister is still collecting a $211,250 salary as a backbench MP and recently skipped the first week of Parliament to travel overseas.

Albanese has confirmed he will seek advice on the legality of Morrison's appointments.

Former prime minister Malcolm Turnbull also slammed revelations that Morrison secretly swore himself into up to five portfolios as "sinister" and "incredible".

Turnbull said he was shocked by the revelations.

Asked if he had ever secretly sworn himself into other minister's portfolio he confirmed he had not.

"No, I think this is one of the most appalling things I have ever heard in our Federal Government,'' Turnbull told ABC TV.

"This is sinister stuff. This is a secret government. What Albanese said today about it is absolutely right."

Turnbull backed calls for an investigation.