A public brawl between Solicitor-General Justin Gleeson, SC, and Senator Brandis came to a head on Monday after Mr Gleeson resigned, saying their relationship was "irretrievably broken".

Shadow attorney-general Mark Dreyfus said on Tuesday Senator Brandis "cannot be trusted" to oversee the process of selecting Mr Gleeson's successor.

In a letter to Mr Turnbull, Mr Dreyfus said the Solicitor-General was a "whole-of-government role and should not be handpicked by an Attorney-General who has shown himself incapable of following due process".

"Through his treatment of Mr Gleeson, he has demonstrated a view of the role of Solicitor-General completely at odds with the way in which this office has operated for a century," he said.

Mr Dreyfus said Senator Brandis "does not accept that it is the role of the second law officer to give frank and fearless advice, whether or not that matches with the government's intent".

He asked Mr Turnbull for a "guarantee that the new Solicitor-General's selection process is not compromised by Senator Brandis's personal direction".

"I ask that the position be advertised, and a selection panel overseen by the secretary of the Department of the Prime Minister and Cabinet be used to determine the shortlist which is put to cabinet," Mr Dreyfus said.

"Anything less will be insufficient to restore the integrity and dignity of the role of Solicitor-General."

This would be a more rigorous selection process than has previously been in place under Labor or Coalition governments.

In a scathing letter to Senator Brandis, Mr Gleeson said his resignation should not be regarded as a backdown from "any position I have taken in relation to matters of controversy between us".

The men had been at loggerheads over a legally binding direction issued by Senator Brandis before the July 2 election which prevented ministers, including the Prime Minister, seeking advice from Mr Gleeson without the Attorney-General's written approval.

Legal experts had expressed concern the directive may mean the Solicitor-General, who holds a statutory office and gives independent advice on matters of national significance as well as appearing in court in high-profile matters, is "frozen out" of advising the government.

Mr Gleeson told an explosive Senate inquiry the "radical" directive was unlawful and he felt a duty to flout it if it conflicted with his duties in office.

But Senator Brandis has said the direction is consistent with the law and historical practice.

He told the Senate inquiry he had referred "all ten" requests for advice from the Solicitor-General he had received since he made the direction, most of which on the same day the request was made.

Mr Gleeson will leave the post on November 7, a day before the Senate inquiry is due to report on allegations Senator Brandis misled Parliament by claiming Mr Gleeson was consulted about the direction.

Mr Gleeson has flatly denied claims he was consulted about the change, but Senator Brandis has insisted his duty to consult did not require him to tell Mr Gleeson about the precise terms of the direction.

Labor has sought to link the Gleeson imbroglio with two other high-profile cases of the government clashing with public servants.

It highlighted the hostile relationship with Human Rights Commission president Gillian Triggs and the sacking of former Agriculture Department secretary Paul Grimes, who questioned Deputy Prime Minister Barnaby Joyce's "integrity".

In a letter to Agriculture Minister Mr Joyce, revealed on Monday, Mr Grimes - a career public servant - observed a "breakdown in our working relationship" amid "Hansard-gate", when the parliamentary record was quietly changed at the minister's request.

Mr Dreyfus said the example was extraordinary, disgraceful and "arose from Barnaby Joyce having manipulated the Hansard, probably falsified the Hansard, to produce a different state of affairs".

"This government cannot take criticism. It does not understand we are stronger as a community, our government is stronger if we learn how to accept criticism. Instead, this government shoots the messenger every time," Mr Dreyfus said.

Foreign Minister Julie Bishop said on Tuesday Mr Dreyfus had politicised the feud.

"It was Mark Dreyfus who dragged the Solicitor-General to a Senate inquiry and tried to use him as a political weapon against the Attorney-General," Ms Bishop said.

Comment was sought from the offices of the Prime Minister and Attorney-General.