Greens leader Adam Bandt said the Parliament must send a "strong message" to Mr Morrison, who he maintains misled MPs by not revealing he had appointed himself to five portfolios during the pandemic.

Speaker Milton Dick on Monday confirmed that he wouldn't refer Mr Morrison to Parliament's privileges committee, after a request from the Greens.

"On the information available to me, it does not seem that a prima-facie case has been made out in terms of the detail that speakers have always required in relation to such allegations," Mr Dick said in a statement to the House of Representatives.

Mr Dick said he understood the Greens' concerns and noted there were other avenues for Parliament to pursue.

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Mr Bandt said he respected Mr Dick's decision, but insisted the Parliament must act to punish the former prime minister.

He said the Greens would support censuring the now Liberal backbencher. A successful motion would not have any practical affect, but it would demonstrate the Parliament's disapproval of Mr Morrison's conduct.

Mr Bandt said the Greens were waiting to see further information about former High Court justice Virginia Bell's independent inquiry into the secret portfolios scandal, but wouldn't necessarily wait until her findings were handed down in November before acting.

"The Parliament has to send a very strong message that prime ministers keeping secret who their ministers are is unacceptable," he said.

"The Parliament was misled. The Parliament was misled and the Parliament needs to send a very strong message that withholding information from the public and the Parliament is unacceptable."

The Bell inquiry was launched after Solicitor-General Stephen Donaghue found that while Mr Morrison's appointment to the resources porfolio was valid under the Constitution, the secrecy surrounding it "fundamentally undermined" the principles of responsible government.

Mr Morrison has repeatedly defended his actions and stressed that he had only ever used his secret powers once - to kill off the PEP-11 gas exploration permit off the NSW coast.