The Solicitor General has been asked to discover precisely what happened, how it occurred, and whether there are any legal ramifications.
Albanese has not ruled out further inquiries and reforms to make sure there cannot be a similar scandal in the future.
Morrison has come under fire from all sides of politics following revelations he had secretly assumed ministerial responsibilities across the portfolios of Health, Home Affairs, Resources, Treasury and Finance portfolios.
He has claimed this was done to provide an extra layer of security during the COVID-19 pandemic, should a minister be struck down by the disease.
However, the assumption of different ministerial roles – usually without the existing minister’s knowledge – was spread out over a number of months.
Morrison has said he used his emergency powers only once, to overrule Keith Pitt’s approval of a gas project, something he acknowledged was unrelated to the COVID-19 pandemic.
Morrison said the secrecy of his actions was necessary in order to not undermine the ministers.
Former Home Affairs Minister Karen Andrews has called for the former prime minister to leave Parliament after the revelations were made public.
Opposition Leader Peter Dutton has declined to join her, saying the process needed to run its course.
Albanese’s language on the matter has also been strong, accusing Morrison of a “power grab” and of an “unprecedented” attack on Australian democratic norms.
There has been no suggestion Morrison’s actions were in any way illegal or unconstitutional.