"I have nothing to say to him.
"This is totally unacceptable, For a prime minister to behave in this manner undermines everything that a federal government constitutionally should stand for."
Albanese called him a "stealth bulldozer" and said that Morrison and those in his government need to be "held to account".
"This has been government by deception," Albanese told reporters in Canberra.
"He told us he was a bulldozer and his Coalition colleagues just shrugged their shoulders and carried on.
"A misleading of parliament as to who was holding what portfolios."
Albanese said the former prime minister had trashed democracy, adding that he couldn't conceive of how Morrison's plans "avoided scrutiny".
Albanese said the appointments were made by the Government-General on the advice of Morrison under Section 64 of the Constitution.
"That is the advice I have received," he explained.
While Albanese was unable to address the "legality" of Morrison's actions, he confirmed that he's sought advice from the Solicitory-General, which will be available next Monday. When asked whether Albanese was critical of the Governor-General's role in Morrison's appointments, the Prime Minister said "it's very clear" that the responsibility was mainly with the Morrison government.
'That was an error': ScoMo responds
Earlier, Morrison made a surprise call to a radio station to address the revelations for the first time.
Morrison called into Ben Fordham's 2GB radio show this morning and admitted it was an "error" not telling the former finance minister Mathias Cormann that he had secretly appointed himself to the portfolio.
Morrison said he had called the former leader of the government in the Senate to apologise.
"That was an error and an oversight and I've apologised," he told 2GB radio.
Cormann discovered over the weekend that Morrison had appointed himself to the portfolio without addressing the change with him.
Morrison used a secret mechanism that allowed him to appoint himself to a portfolio without needing to make a public announcement.
Of the five portfolios, only then-health minister Greg Hunt is known to have been made aware that Morrison was becoming a co-minister.
Morrison said he thought the fact he had appointed himself to jointly have power in the finance portfolio had been "sorted" between his and Cormann's offices, but admitted he never bothered to tell his colleague.
"Things were moving very quickly at the time,'' he said.
"None of us are perfect. There was no sense of bad faith in it."
But he defended the decision to "safeguard" the portfolios as prudent, given the risk a minister could be taken down by Covid and be unable to administer their portfolio.
Before the total number of portfolios taken over by the then-prime minister was confirmed, Morrison said it was "not his recollection" that he had appointed himself to any more than three, but said he was checking.
"I'm pursuing that, but not to my recollection. There were a number (of other portfolios) that we considered at the time to safeguard," he said.
Albo: 'I'll run a good, orderly government'
Albanese also staunchly promised to run an "orderly" government, that stands in "stark contrast" to the former "rabble".
"I can confirm that no-one was appointed to different portfolios in secret," he said.
"I can confirm that we had proper processes and papers presented before that Cabinet.
"I'll continue to run a good, orderly government that stands in stark contrast to the rabble and the chaos and the undermining of parliamentary democracy of our predecessors."
Current Leader of the Opposition, Peter Dutton, is slated to address the secret appointments later on Tuesday.
