Royal commissioner Dyson Heydon has delayed his decision on union applications that he stand down on the grounds of “apprehended bias”.

Heydon indicated on Friday he hoped to make his ruling on Tuesday.

But a statement issued late Monday said: “Mr Heydon is still considering his ruling … The royal commission will make a further statement on the timing of commissioner Heydon’s decision in due course”.

In a further disruption of the commission, a public hearing scheduled for Wednesday involving the CFMEU New South Wales branch has been postponed to a date to be fixed.

The application for Heydon to quit follows his acceptance of a invitation to deliver the Garfield Barwick address, sponsored by lawyers' branches of the Liberal Party. Heydon eventually withdrew from the function, telling the commission he had “overlooked” its Liberal Party connection.

The Coalition has strongly backed Heydon remaining in his post; the federal opposition has said he should disqualify himself.

If Heydon stood down, the government would have to either abandon the commission or find a replacement, who might have to redo part of the work already carried out.

If Heydon continued, Labor and the unions would argue that the commission’s findings were tarnished – especially any criticism of Opposition Leader Bill Shorten, who gave evidence.

Michelle Grattan does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond the academic appointment above.