High Court judge to head Morrison inquiry

It followed his receipt of an opinion from the solicitor-general which found Mr Morrison did not break any laws in secretly taking on the portfolios between 2020 and 2021, but that it went against the principles of "responsible government".

The inquiry report be will handed down on November 25.

Along with Mr Morrison's ministerial appointments, the inquiry will also examine the functioning of departments, government business enterprises and statutory bodies.

The terms of the inquiry were agreed to by federal cabinet on Wednesday.

Mr Albanese said the inquiry would provide transparency about the controversial appointments.

"We need to have a quick and appropriate inquiry which is not about the politics but about how this happened, why it happened, who knew about it," he told reporters in Sydney.

"We need to have transparency in the process because our system of parliamentary democracy relies upon conventions, relies upon the Westminster system of checks and balances."

Ms Bell served on the High Court for 12 years, following her appointment in 2009.

Mr Albanese said the appointment of Ms Bell as the inquiry's head would ensure public confidence.

The inquiry would not have the powers of a royal commission, but the prime minister said other measures would be considered if witnesses were not cooperating.

"I would find it extraordinary if anyone refused to talk to a former High Court judge who is, I think, beyond reproach," Mr Albanese said.

"I'm certain that this appointment will be seen for what it is and that people will cooperate by giving information."

Mr Morrison says while he should have let his colleagues know of his actions, he only used his extra powers in one instance - as resources minister, blocking the PEP-11 gas project off the NSW coast.

Former prime minister Malcolm Turnbull said this week the inquiry needed to go beyond the conduct of Mr Morrison and examine the prime minister's department and the governor-general's office.

He was astonished there was apparently no pushback to Mr Morrison when he "embarked on his bizarre secret accumulation of power".

Another former prime minister Tony Abbott has described Mr Morrison's conduct as "highly unconventional, highly unorthodox and shouldn't have happened".

Speaker Milton Dick has rejected a request from the Greens to refer Mr Morrison to the parliamentary privileges committee, advising there wasn't enough evidence to establish he had knowingly and deliberately misled parliament.

According to the solicitor-general, 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".