Labor to push on Senate bid to oust Dyson Heydon

Labor is expected to push ahead with a motion asking Governor-General Peter Cosgrove to sack trade union royal commissioner Dyson Heydon when the Senate resumes on Monday.

Labor plans to ask the Senate to back its move after Mr Heydon rejected union arguments that he disqualify himself from overseeing an inquiry into trade union corruption because he planned to address a Liberal Party event.

Labor Senate leader Penny Wong says the action is regrettable but necessary.

"It is regrettable that the Senate has to consider such a resolution given the circumstances, but given that Tony Abbott is refusing to act ... really it's up to the parliament to act," Senator Wong told ABC radio on Tuesday.

The federal government has written to crossbench senators urging them not to back the motion.

Government Senate leader Eric Abetz warned the move risks encroaching on the separation of powers and, in any event, would have no legal effect.

"If they've got a problem with Mr Heydon's decision they have the right to go to the courts to appeal that decision," he said on Wednesday.

Unions are considering appealing to the Federal Court in a bid to remove Mr Heydon.