A plethora of encrypted texts revealed by Nine Newspapers on Sunday show Mr Pezzullo using a political back channel to contact two former Liberal prime ministers.
The texts indicate he used Liberal powerbroker Scott Briggs to wield influence, including suggesting ministerial sackings and which MP should become minister of his department.
More messages revealed on Monday showed Mr Pezzullo trying to convince the Liberal government to criminalise reporting stories sourced from whistleblowers if a department deemed them damaging to national security.
Prime Minister Anthony Albanese confirmed Mr Pezzullo had agreed to stand aside during the investigation.
Former Australian public service commissioner Lynelle Briggs will conduct the inquiry and Stephanie Foster will run the department in his absence.
"He has agreed to stand aside, that action is appropriate," Mr Albanese said.
"We'll await the findings of the investigation which we will expedite, we have a cabinet meeting (on Monday) where no doubt I'll be able to get further reports."
But Opposition Leader Peter Dutton - who was home affairs minister when Mr Pezzullo was secretary - defended him and suggested the leaking of text messages should be referred to federal police.
The texts showed Mr Pezzullo suggested Mr Dutton should become the new home affairs minister the night before Scott Morrison ousted Malcolm Turnbull from the prime ministership in 2018.
"(Mr Pezzullo) was able to, in all of his interactions, put the country first … he had a passion for home affairs because he believes very strongly in national security and border protection," Mr Dutton said.
Earlier, a Greens senator and a refugee advocacy body not only called for Mr Pezzullo to quit, but for the department to be shut down.
Greens Senator Nick McKim said it was "an abject failure to understand … the difference between being a public servant and a politician".
"The Greens support abolishing the home affairs department and breaking up its functions to improve accountability and oversight," he told AAP.
Refugee Action Coalition's Ian Rintoul agreed, saying "it is not just Pezzullo that needs to go".
"Pezzullo epitomises the punitive mentality that characterises the home affairs department and is bolstered by Labor's on-going support of Operation Sovereign Borders," he said.
It is not suggested the messages show corrupt or illegal conduct but arguably that Mr Pezzullo overstepped the required impartial nature of heading a government department.
Mr Pezzullo was the first person appointed to head the Department of Home Affairs when it was created in 2017.
The department declined to comment, suggesting any questions about the conduct of a secretary were matters for the government, along with the Australian Public Service Commission.
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