Dyson Heydon says he will decide on his future as the trade union royal commissioner next week after hearing submissions calling for his resignation on Friday.

Justice Heydon said he intended to make the decision by Tuesday.

The former High Court judge conceded he overlooked the connection between the Liberal Party and an event he had previously agreed to speak at in Sydney later this month.

Justice Heydon has so far resisted calls for his resignation on the grounds he was not aware of the event, known as the Sir Garfield Barwick address, was a fundraiser.

Key points: Royal commission into trade unions resumes

Royal commission into trade unions resumes Dyson Heydon hears submissions calling for his resignation

Dyson Heydon hears submissions calling for his resignation Issue is "apprehended bias" or public perceptions of him speaking at a Liberal Party fundraiser

The submissions heard on Friday addressed the issue of "apprehended bias" — what the average person might think after the commissioner's acceptance of the invitation to speak at the Liberal Party event.

Addressing the commissioner, counsel for the Australian Council of Trade Unions (ACTU) Robert Newlinds SC said: "Being prepared to associate yourself with a party fundraiser was sufficient to engender a disquiet that you might be partisan."

Mr Newlinds explored in detailed emails sent between the organiser of the event and Justice Heydon, pointing out that in one, the subject line included "Liberal Party of Australia NSW" and that the invitation had the Liberal logo and brand:

"The hypothetical reasonable observer would really be in no doubt that you understood that this was a Liberal Party function and that you understood it was a fundraiser of some type, and that's because the hypothetical observer would naturally assume that you would read the email and, even if scanning it, you would pick up those facts."

Mr Newlinds also looked at a later email in which Justice Heydon's assistant told event organisers that he would be withdrawing his services.

Part of the email read:

If there is any possibility that the event could be described as a Liberal Party event he will be unable to give the address, at least while he is in the position of royal commissioner.

The unions argued that the last part of the sentence shows that Justice Heydon was still willing to speak at some point in the future at a Liberal Party event and therefore he was affiliated or associated with the Liberal Party.

Unions say royal commission is 'politically charged'

A written submission lodged on behalf of the ACTU, Unions NSW and four unions said Justice Heydon should recuse himself and resign his commission "on the grounds that he is unable to afford any union or any person associated with any union procedural fairness as a result of his apprehended bias".

It quoted a past case, Ebner v Official Trustee in Bankruptcy (2000), to back its argument:

"... a judge is disqualified if a fair-minded lay observer might reasonably apprehend that the judge might not bring an impartial mind to the resolution of the question the judge is required to decide. That principle gives effect to the requirement that justice should both be done and be seen to be done, a requirement which reflects the fundamental importance of the principle that the tribunal be independent and impartial."

The submission described the royal commission as "politically charged", and said a fair-minded observer could reasonably believe the commissioner might not bring an impartial mind to the issues before the commission:

"Had the work of the commission not been so politically charged then perhaps an agreement to speak at a party political event during the course of a royal commission would create no real problem or difficulty, or no real problem or difficulty of any moment. But that is not the present case."

On Thursday, Federal Opposition Leader Bill Shorten said he would not block moves to appoint a replacement to the Royal Commission into Trade Union Governance and Corruption, if Justice Heydon did rule himself out.

Space to play or pause, M to mute, left and right arrows to seek, up and down arrows for volume. Watch Duration: 6 minutes 28 seconds 6 m Dyson Heydon defers decision on bias accusations

Counsel for the Construction, Forestry, Mining and Energy Union (CFMEU) John Agius also suggested during the hearing that an email which was tendered to the commission was doctored because it originally contained an attachment named "state donation compliance" which made it clear that it was a Liberal fundraiser.

However, Mr Agius later rescinded the allegations and agreed that the attachment had not been included when the email had been forwarded.

Mr Agius also said any apprehension of bias by Mr Heydon was unacceptable given the importance royal commissions play in Australia.

"If there is an apprehension of bias in relation to a royal commission then that infects not just any possible findings of that royal commission, whether they be favourable or against any particular party, it infects the whole role of royal commissions in our society," he said.

ACTU says hearing shows commissioner is biased

ACTU secretary Dave Oliver said outside the commission that the union still believed the commissioner had shown bias and should be stood down.

"I would have to say on the face of what we've seen today and you've now had an opportunity to read the submissions that have been put, the fact is that Dyson Heydon has known for over 12 months that this has been a Liberal Party event and a Liberal Party fundraiser," he said.

"That in anyone's mind would show that there is an apprehension of bias, and that's all that needs to be proved here for the commissioner to step down from this hearing."

He also called on Prime Minister Tony Abbott to close the royal commission down.

"The ACTU and the trade union movement has long said that this royal commission is a multi-million-dollar, taxpayer-funded exercise to weaken the political opponents of Tony Abbott and the Liberal Party and, after today, we are now calling on Tony Abbott to shut this farce down," Mr Oliver said.

"Shut this royal commission down this afternoon. He can do that. That's what we're asking him to do."