Scott Morrison could be dragged before an inquiry with the same powers as a Royal Commission if he declines to co-operate with an independent probe into his five secret ministries to be led by former High Court judge Virginia Bell.

Announcing the second inquiry into the behaviour of the former government in as many days, Prime Minister Anthony Albanese said the Bell Inquiry would examine the role played by Governor-General David Hurley as part of its pursuit of how the ghost ministries were allowed to happen, why they were kept secret, who else knew and if there were any other implications.