Trade union royal commissioner Dyson Heydon has delayed his decision about whether to stand down from the position.

Unions have applied to Justice Heydon to remove himself from the Royal Commission into Trade Union Governance and Corruption amid allegations of bias and a conflict of interest.

Justice Heydon initially said he would deliver his decision on Tuesday, but on Monday afternoon he released a statement saying he was still considering the ruling and would announce the timing in due course.

"Mr Heydon is still considering his ruling, which will now not be delivered on that date," the statement said.

"The royal commission will make a further statement on the timing of Commissioner Heydon's decision in due course."

The commission has also postponed a public hearing involving the CFMEU NSW Branch that was scheduled to take place on Wednesday.

Prime Minister Tony Abbott is continuing to back Justice Heydon to stay in his position.

Mr Abbott said Justice Heydon was a man of utmost integrity and he was carefully considering submissions.

"I can't imagine that it's going to be delayed too long because these are things which are inherently decided, best decided quickly," he said.

Justice Heydon has been under pressure since it was revealed he had accepted an invitation to speak at a Liberal Party fundraiser in Sydney this month.

The former High Court judge withdrew from the event but acknowledged he had overlooked its political links.

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.

A written submission lodged on behalf of the Australian Council of Trade Unions (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".

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.

Federal Opposition Leader Bill Shorten, who was himself called to appear before the commission, said he would not block moves to appoint a replacement if Justice Heydon did rule himself out.

In a statement released on Monday, the ACTU called on the royal commission to be shut down, calling it a "political witch hunt".