Home Affairs secretary Mike Pezzullo has been stood down amid an investigation into leaked text messages he sent to a Liberal Party powerbroker.

A plethora of encrypted texts revealed by Nine Newspapers on Sunday night show Mr Pezzullo using a political back channel to 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.

A second tranche of messages leaked on Monday show Pezullo suggesting the Coalition government should strengthen its ability to take legal action against stories sourced from whistleblowers.

Prime Minister Anthony Albanese confirmed on Monday that Pezzullo had agreed to stand aside during the investigation. It will be led by would be former Australian public service commissioner Lynelle Briggs.

Home Affairs Minister Clare O’Neil, who initially referred the matter to the public service’s oversight body, then asked Pezzullo to stand down.

“He has agreed to stand aside, that action is appropriate,” Albanese said.

“We’ll await the findings of the investigation, which we will expedite. We have a cabinet meeting [later on Monday] where no doubt I’ll be able to get further reports about that.”

Albanese said he believed Pezzullo’s move was “appropriate”, given the allegations.

Opposition Leader Peter Dutton said Pezzullo had always been “professional” while department secretary when Dutton was home affairs minister.

“I found him especially, as a person who had served both a Labor government and a Liberal government, he has plenty of friends on the Labor side,” he said.

Earlier, a Greens senator and a refugee advocacy body called for Pezzullo to quit.

Greens Senator Nick McKim said it was “an abject failure to understand … the difference between being a public servant and a politician”.

“These messages along with years and years of arrogance, of failure to accept responsibility, of failure to understand the principle of accountability … a litany of scandals and failures he has overseen in the Home Affairs department … [show] his position is untenable,” he told ABC Radio.

“If he’s not working on his resignation letter to Albanese, he certainly should be.”

Texts showed Pezzullo suggested the night before Scott Morrison took the PM role from Malcolm Turnbull in 2018 that Dutton should become home affairs minister.

According to the messages, he suggested the Liberals sack former defence minister Christopher Pyne, labelled another former defence minister, Marise Payne, “completely ineffectual” and “a problem”, and said he “almost had a heart attack” when Julie Bishop was linked with a tilt at the prime ministership in 2018.

Others show Briggs directly asking if Pezzullo had any messages he wanted him to convey before a dinner with Morrison and Turnbull.

It is not suggested the messages show corrupt or illegal conduct but arguably that Pezzullo overstepped the required impartial nature of heading a government department.

Pezzullo was the first person appointed to head the Home Affairs Department when it was created in 2017.

Refugee Action Coalition’s Ian Rintoul said the government should sack him, but added Pezzullo was a “symptom of the sick system Labor has kept in place”.

“It is not just Pezzullo that needs to go,” he said.

“Pezzullo epitomises the punitive mentality that characterises the Home Affairs department, and is bolstered by Labor’s on-going support of Operation Sovereign Borders.”

– with AAP