Former high court judge Virginia Bell has been welcomed as a strong choice to lead an inquiry into Scott Morrison's secret ministerial appointments.
But the Greens say the Labor government has failed to give her sufficient powers to summons uncooperative witnesses and compel the production of documents.
And the Liberals say the government should be focusing on other issues like the cost of living and not dwelling on the past.
Prime Minister Anthony Albanese revealed details of the inquiry at a media conference on Friday.
Mr Morrison secretly took on five ministerial portfolios between March 2020 and May 2021, which he said was necessary to deal with "multiple crises" including the COVID-19 pandemic.
He insists no extra ministerial powers were exercised apart from, as resources minister, blocking the PEP-11 gas project off the NSW coast.
The solicitor-general found Mr Morrison did not break any laws, but that his action went against the principles of "responsible government".
Mr Morrison's colleagues have also been critical of him for not telling them of his action, for which he has apologised.
Asked whether Mr Morrison would cooperate with the inquiry, Liberal deputy leader and former ministerial colleague Sussan Ley said it was up to him, but she noted he had released two "detailed statements" already.
The inquiry will look at the implications arising from the appointments, including on the functioning of departments, the structure of the ministry, the accountability of minsters to the parliament and public confidence in government.
Mr Albanese said the November 25 reporting date had been set to allow for the final week of parliament for the year to legislate any recommendations out of Ms Bell's report to improve transparency and accountability.
Greens justice spokesman David Shoebridge said she needed more powers, but Mr Albanese said if Ms Bell needed anything he would consider her requests.
"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.
Senator Shoebridge said handing the administration of the inquiry to the attorney-general's department - when that department "green-lighted this entire fiasco" - represented a conflict of interest.
Ms Ley said Mr Albanese was "obsessed and consumed by the politics of the past" rather than focused on addressing the rising cost of living.
