Unions are seeking advice on whether to go to court to force the end of the royal commission investigating corruption within their ranks.
Prime Minister Tony Abbott has stood by royal commissioner Dyson Heydon in the wake of revelations the former High Court judge had accepted an invitation to speak at a Liberal Party fundraiser in Sydney later in August.
Mr Heydon withdrew from the function on Thursday, a day after he was told by the organiser in an email that it was being run by a Liberal Party branch.
It's understood the ACTU is seeking legal advice on whether there was scope for court action to end the inquiry.
As an initial step, ACTU president Ged Kearney and secretary Dave Oliver have written to Mr Abbott calling on him to wrap up the royal commission.
"The royal commission into trade union corruption has no claim to independence, impartiality or adherence to due process and must be terminated immediately," they wrote.
"It is untenable for Justice Dyson Heydon, who you appointed personally to oversee the royal commission, to continue in his role following the revelation he accepted an invitation to appear as guest speaker at a Liberal Party fundraising event."
They said Mr Heydon himself had defined "apprehended bias" in a High Court judgment, when he wrote: "the appearance of departure from neutrality is a ground of disqualification".
The appearance of bias and partisan behaviour tainted all findings of the royal commission, they said.
Mr Abbott told reporters in Adelaide Mr Heydon was a "man of great integrity", shown by the fact he withdrew from the event as soon as the royal commissioner realised it had some association with the Liberal Party.
Mr Heydon declined to comment on the furore when he presided at a hearing of the commission in Sydney on Friday.
Asked whether all correspondence relating to the dinner should be publicly released, Mr Abbott said: "That is really a matter for the royal commissioner."
Cabinet minister Christopher Pyne queried why Mr Heydon had been invited to speak at all.
"Why a barrister in the Liberal Party thought it was a good idea to invite him is beyond me, but Dyson Heydon's doing a terrific job," he said.
Opposition Leader Bill Shorten said the fact that Mr Heydon had been billed as a guest speaker at a Liberal fundraiser was "the smoking gun of political bias".
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