The Australian Council of Trade Unions (ACTU) will go ahead with an application to disqualify trade unions royal commissioner Dyson Heydon.

Justice Heydon has conceded he overlooked the connection between the Liberal Party and an event he had previously agreed to speak at in Sydney later this month.

The royal commissioner will hear the application, about himself, on Friday.

The ACTU earlier this week interrupted the Royal Commission into Trade Union Governance and Corruption and asked Justice Heydon to produce correspondence relating to his cancelled Sir Garfield Barwick lecture.

It was revealed he initially agreed to the talk in April 2014 and was contacted again by the coordinator of the speech in March 2015.

"I overlooked the connection between the person or persons organising the event and the Liberal Party," Justice Heydon said about the email he received earlier this year.

Key points: ACTU will apply to have commissioner disqualified

ACTU will apply to have commissioner disqualified Dyson Heydon previously agreed to speak at Liberal-linked event

Dyson Heydon previously agreed to speak at Liberal-linked event Union alleges inquiry is "witch hunt"

Union alleges inquiry is "witch hunt" Heydon to hear application on Friday

The union movement's attempt to disqualify the royal commissioner for bias follows months of labelling the inquiry a "political witch hunt".

"The ACTU has always maintained that the royal commission is a political witch hunt by Tony Abbott designed to weaken his political opponents," secretary Dave Oliver said in a statement.

"When it came to light that commissioner Dyson Heydon had agreed to speak at a Liberal Party fundraiser, we called on Prime Minister Tony Abbott to shut down the royal commission.

"Given Tony Abbott has failed to act, the ACTU must now take further action."

If the move is unsuccessful the unions will appeal to higher courts.

Government defends Heydon; says Shorten 'ripped off workers'

Mr Abbott has repeatedly defended Justice Heydon and attacked Labor for their "vicious slander" during Question Time.

"All members opposite are doing with this increasingly shrill and hysterical and hypocritical attack on the royal commissioner is demonstrate how much they have to hide ... and based on the evidence before the royal commission so far, there is a very great deal to hide," Mr Abbott said.

"The Leader of the Opposition himself has been exposed as someone who was supposed to represent workers, but he ripped off the workers to help himself.

"[Dyson Heydon] is an honourable man. He should be allowed to get on with his job and members opposite should stop trying to protect and defend the indefensible."

"It's true that the royal commissioner was invited to address this gathering, which was not a fundraiser, it was associated with the Liberal Party, but to quote from the email that he received in April last year: 'We organise forums on matters of professional and legal policy interest'."

Mr Shorten hit back at the Prime Minister's comments.

"I'll put my record up against Tony Abbott's any day of the week," he said in a statement.

"My record of standing up for workers, better pay and safer workplaces versus Tony Abbott's only contribution to industrial relations: WorkChoices.

"All he wants to do is cut workers' pay and conditions.

"Under Tony Abbott, there are now more than 800,000 people unemployed for the first time in 20 years."