Prime Minister Anthony Albanese will be briefed on Monday afternoon on legal advice about whether Scott Morrison breached any rules after he appointed himself to five portfolios.

Mr Albanese said he intended to take the rare step of publicly releasing advice from the solicitor-general on Tuesday, following a cabinet meeting.

Secretary of the Department of Prime Minister and Cabinet Glyn Davis had already received the advice, which was handed over on Monday morning.

“I intend to release that advice so that people can see it and be transparent about it, and we will,” Mr Albanese said in Sydney.

“We have cabinet meetings tomorrow. I think politeness and proper process mean that they should have access to it. I will do that and I intend to release the advice tomorrow.”

It comes amid growing calls for an inquiry into the former Liberal prime minister’s decision to secretly appoint himself as a joint minister in the health, finance, treasury, home affairs, industry, science, energy and resources portfolios between March 2020 and May 2021.

• Unusual disclaimer added to Morrison ministry list

One of his decisions, as joint resources minister, was to block the PEP-11 gas exploration licence off the NSW coast after the then resources minister Keith Pitt approved the project.

The final decision is the subject of a Federal Court appeal.

Mr Albanese said there remained questions about Mr Morrison’s ministries.

“There is a basic fundamental weakness in checks and balances – if no one knows who the minister is, then how can they be held to account for decisions which are made?” he said.

“There is a question of legality. There hasn’t been a suggestion of illegality but there have been questions raised about how this could occur, how it fits in with the conventions.”

He has flagged a separate review into Mr Morrison’s actions – a move that won support from Liberal backbencher Bridget Archer.

She said she had an open mind about how such an inquiry would be conducted.

“Australians generally agree that we don’t want to see this sort of situation occur into the future, so we need to examine how we got here and how we stop it happening going forward,” she told ABC Radio.

Ms Archer said while she was reluctant to ask for other MPs to resign – as former home affairs minister Karen Andrews has urged Mr Morrison to do – the former PM should “reflect” on his behaviour.

“It also is forcing other colleagues to … kind of having to defend themselves and their own records. And I think that that’s unfair,” she said.

“[Mr Morrison] should reflect on that and, and certainly consider whether it’s the best thing for him to do going forward.”

Greens leader Adam Bandt wants an inquiry to examine Mr Morrison’s conduct and whether he misled the parliament or pressured the governor-general or public service.

“The longer that this goes on, the more questions that are raised about exactly how much damage has been done to Australian democracy,” Mr Bandt told ABC News.

“You’re entitled to expect that when the prime minister stands up and says ‘here’s who the ministers are in my parliament, here’s what my responsibilities are’, you’re entitled to expect that they are telling the truth and it’s becoming clear day by day that that’s not the case.”

The Greens have already asked House of Representatives Speaker Milton Dick to refer Mr Morrison to the powerful privileges committee over the scandal.

Mr Bandt said an inquiry would also need to examine who was asked by Mr Morrison to keep his ministries secret from the public and most of his colleagues.

“One of the things that we don’t yet know is whether or not that was done at Scott Morrison’s requests, whether or not he made requests of the governor-general to keep some of these appointments secret,” he said.

“Similarly, with respect to his own department, what did … the former prime minister do?”

– AAP