Nick McKim says Mike Pezzullo should to resign or be sacked immediately

Nine newspapers reported Mr Pezzullo had sent more than a thousand leaked encrypted messages over five years to former vice-president of the NSW Liberals Scott Briggs. The Canberra Times has not seen the messages.

Greens immigration and citizenship spokesperson Nick McKim said that "Mr Pezullo's time as a senior public servant needs to end and it needs to end today".

Senator McKim called on Prime Minister Anthony Albanese to demand Mr Pezzullo's resignation or sack him.

"Throughout his time as secretary of the Department of Home Affairs he has overseen a litany of governance failures and shown complete contempt for the principle of accountability," Senator McKim said.

"His brazen attempts to manipulate the political process and his failure to respect the boundaries between politics and the public service mean that his position is untenable."

"If Mr Pezzullo wants to play in the political sandpit then he should stand for Parliament."

The text messages allegedly show Mr Pezzullo sending messages through Mr Briggs to two former Liberal prime ministers.

Some messages to Mr Briggs allegedly show him advocating for now Opposition Leader Peter Dutton to be appointed as Home Affairs minister the night before Scott Morrison won a leadership spill against then-prime minister Malcolm Turnbull.

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.

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Mr Dutton told reporters on Monday that he had always found Mr Pezzullo to be "professional".

"I found him - particularly as a person who had served both a Labor government and a Liberal government, he has plenty of friends on the Labor side, he was obviously deputy chief of staff to Kim Beazley - and he conducted himself in a thoroughly professional way in my dealings with him, and that was my experience of dealing with Mr Pezzullo," he said.

Senator McKim also criticised the Prime Minister for reappointing Mr Pezzullo as Home Affairs secretary in June last year, dubbing it a grievous mistake.

The Greens senator said that should Mr Pezzullo exit the top public service position, "that must not mean a sideways shuflfle, a golden handshake or a cushy diplomatic post".

Independent member for Mackeller Dr Sophie Scamps also said that Mr Pezzullo's position in the public service was untenable and that "it is clearly time for new leadership at the Department of Home Affairs".

"An apolitical independent service is one of the important pillars of our democracy," she said.

"When taxpayer funded public servant leaders who are supposed to implement the policies of the government of the day stray from public service into politics - we all lose."

- with AAP