Attorney-General George Brandis and the government's chief legal adviser are set for a public showdown over allegations Senator Brandis misled Parliament, after both men agreed to front an explosive Senate inquiry into the claims.

The country's two most senior lawyers are locked in an extraordinary brawl over a binding direction issued by Senator Brandis before the election requiring all ministers, including the Prime Minister, to obtain his permission before seeking advice from Solicitor-General Justin Gleeson, SC.

In a submission last week to a Senate inquiry, Mr Gleeson flatly denied claims by Senator Brandis in Parliament that he was consulted about the direction and said he would have opposed it "in the strongest terms".

It prompted calls from Labor for Senator Brandis to resign for misleading Parliament.