Prime Minister Anthony Albanese revealed on Tuesday that Mr Morrison had appointed himself to the finance, treasury, health, home affairs and resources portfolios between March 2020 and May 2021.
One of Mr Morrison's decisions as resources minister - in relation to the PEP-11 gas project off the NSW coast - is before the Federal Court.
The solicitor-general is preparing advice for Mr Albanese to be delivered on Monday on whether there are other legal issues at play relating to Mr Morrison's actions.
"I believed it was necessary to have authority, to have what were effectively emergency powers, to exercise in extreme situations that would be unforeseen, that would enable me to act in the national interests," Mr Morrison told reporters in Sydney on Wednesday.
"Where there were authorities or powers that could be established, there was a clear expectation that I, as prime minister, would have sought to put those in place to protect the country and lead us through what was a very difficult period."
Mr Morrison added the lawful move wasn't a power grab as he never used the powers or overruled ministers.
"As prime minister, only I could really understand the weight of responsibility that was on my shoulders," he said.
One of Mr Morrison's former ministerial colleagues, Karen Andrews, who was unaware she was being shadowed in her role by the Liberal leader, has called on him to quit parliament.
"The Australian people have been let down, they have been betrayed," she said.
A number of crossbenchers have flagged referring Mr Morrison to parliamentary committees.
Independent MP Sophie Scamps has called for the matter to be referred to parliament's privileges committee, which reports on complaints of breaches of privilege or contempt.
"Is it a precedent for future behaviour by future leaders who feel that they may want to have more power?" she asked on the ABC on Wednesday.
"Or will it be something that we regard as a misuse of power and privilege?"
Independent senator Jacqui Lambie wants the saga referred to the Senate's legal and constitutional affairs committee which can review the legislative framework that enabled Mr Morrison's actions.
Mr Morrison said he was happy to cooperate with any "positive process" that examined the government's pandemic response.
He apologised to his colleagues for having secretly sworn himself into their portfolios but launched a staunch defence of his actions, saying the COVID-19 pandemic required a unique response.
"It was a very extraordinary time that tested every sinew and fabric of government, not just at a federal level but at a state level as well and indeed tested the very fabric and sinew of Australian society," he said.
"We took decisions - I did as a prime minister, we did as a cabinet - at federal and state level that some of us would never have dreamed that we would ever have to make."
But constitutional lawyer Anne Twomey says legal systems were already in place, with acting ministers able to be appointed when a minister is sick or on leave.
"It seems there's this presidential view of, 'Hey, I'm the leader, therefore I must have responsibility for everything'," she said on Sky News.
"That's a real denial of the actual system of government we've got. The prime minister, at most, is the first amongst equals."
Labor is considering ways to make ministerial appointments more transparent.
Mr Albanese said the actions of his predecessor followed a pattern of secrecy.
"Our democracy relies on people being open and transparent about what's going on (and) people being accountable and that's why this is such a shocking series of revelations," he told radio 4BC.
Deputy Liberal leader Sussan Ley attacked the prime minister for not focusing on the cost of living and skills shortages.
"Australians want him to focus on the issues in their lives. Nothing in this is going to bring down your power bills," she told Sky News.
Home Affairs Minister Clare O'Neil said intelligence chiefs were unaware of Mr Morrison's self-appointment to the important role.
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