Attorney-General George Brandis insists his relationship with the nation's second law officer is cordial and workable, despite a dispute between the pair over who can seek government legal advice.
Labor has called for Senator Brandis to resign over the spat with Commonwealth Solicitor-General Justin Gleeson.
The attorney acknowledged there was a difference between he and Mr Gleeson on the new rules.
"The fact is the ordinary relationship between Mr Gleeson and me as two senior professional lawyers has not been compromised or affected whatsoever," he told Sky News on Thursday.
Senator Brandis told the parliament in September Mr Gleeson had been consulted during a meeting in November 2015 over new guidelines ruling that no-one in government, including the prime minister, could seek the solicitor-general's advice without the minister's permission.
In a submission to a Senate inquiry, released on Wednesday, Mr Gleeson rejected that claim, saying Senator Brandis did not indicate he was considering issuing a legally-binding direction.
"It's quite clear that George Brandis has lied to the parliament," shadow attorney-general Mark Dreyfus told ABC radio.
"And he's now lying about lying because he's still claiming he did consult even in the face of Justin Gleeson having put in a submissions to the Senate committee saying in unequivocal terms, 'I was not consulted'."
Senator Brandis said he regarded the whole affair "purely an administrative issue that Mr Dreyfus has vastly overcooked".
Mr Gleeson told the Senate inquiry he had not been consulted on significant changes to the government's laws to strip citizenship from terror suspects and not at all on a marriage equality proposal "under active consideration by the government" in November.
He had also raised concerns with Senator Brandis around statements from the attorney-general and prime minister about the release of letters from 1975 between then-governor-general Sir John Kerr and the Queen.
"Where public statements are made about the content of advice to the government on matters of the highest importance, it is critical that they do not convey that advice has come from the solicitor-general is that is not the fact," Mr Gleeson wrote to Senator Brandis in November.
Mr Dreyfus later on Thursday said both the lack of consultation on the changes to MPs' ability to seek legal advice, and the citizenship bill, were "very serious matters".
"It's an extraordinary event - unprecedented in the history of the federation - that there should be this kind of public dispute now before a Senate committee," he told reporters in Melbourne.
Mr Dreyfus rejected Senator Brandis' suggestion that his relationship with Mr Gleeson was cordial, arguing correspondence between the two last year showed "relations are quite frayed".
The attorney-general was "squirming and slithering around trying to pretend he did not mislead parliament", Mr Dreyfus said.
Senator Brandis on Thursday afternoon released a ministerial briefing document from April, which stated his department considered his consultation with the solicitor general had meet legal obligations.
