Heydon defers ruling on inquiry role

Dyson Heydon has given himself more time to decide if he'll bow to union demands and quit as the head of the royal commission into union corruption.

The commission will reconvene on Tuesday, when Mr Heydon could reveal his future.

The ACTU, Australian Workers Union and the Construction, Forestry, Mining and Energy Union on Friday argued he could not continue to lead the probe into union corruption.

They've mounted comprehensive arguments about why his decision to accept an invitation to speak at a Liberal Party fund-raising event could lead to a perception of political bias.

Mr Heydon, who later withdrew from the event, has admitted he "overlooked" a connection between the Sir Garfield Barwick address and the Liberal party, and never understood the dinner to be a fundraiser.

But the unions, in their bid to push him out of the commissioner's role, have focused heavily on email evidence from the event's organiser, which they say could have left Mr Heydon in no doubt about the nature of the event.

ACTU senior counsel Robert Newlinds told Mr Heydon the report he's been tasked with producing on union corruption will have no credibility if there's a perception of bias.

"It can't be allowed to happen that people can just walk around after the report and say `Oh well, don't worry about that report, that was old Mr Heydon and he was biased, he told us he was biased'," Mr Newlinds said.

"The submission is that the reasonable observer might apprehend that you might not be able to bring an impartial mind to the issues at hand."

Counsel for the AWU, Herman Borenstein QC, told the commission that once Mr Heydon had accepted the invitation "that taints the work that the commissioner does in relation to this commission".

John Agius, for the CFMEU, said it was implausible that Mr Heydon didn't understand the political nature of the event, given the branding and content of emails he had received from an event organiser.

"You've always known that it was a Liberal Party event, he's known that from April 2014, the hypothetical observer might think," he told the commission.

Mr Agius told the commission emails released by it appeared to have been "doctored" because they dropped reference to political donation disclosure and "Liberal Party of Australia New South Wales division lawyers branch and legal policy branch".

But after receiving advice from commission staff, Mr Agius later admitted there was a technical explanation for why the words and attachment could not be seen.