Thomson under further pressure

The opposition says a dismissal of MP Craig Thomson's claims by the Fair Work boss about his deputy is grounds for a referral to the privileges committee.

The head of Fair Work Australia (FWA) says there's no evidence his deputy interfered with a inquiry into federal MP Craig Thomson, prompting opposition calls for the matter to be examined by the powerful house privileges committee.

FWA president Justice Iain Ross also told a Senate hearing on Monday Mr Thomson's claims a FWA investigation into the MP's time as national secretary of the Health Services Union (HSU) was biased should be tested in a court of law.

The authority's vice president Michael Lawler is the partner of Kathy Jackson, the HSU official who replaced Mr Thomson and then blew the whistle on financial practices as the union.

"No one has provided me with any evidence to support the allegation that vice president Lawler has sought to influence, in any way, the HSU investigations," Justice Ross told the hearing in Canberra.

"The vice president has assured me that the imputations of misconduct by him arising from Mr Thomson's statements are false."

During his testimony Justice Ross, who took up his position on March 1, said he did not plan to investigate the matters raised by Mr Thomson in a statement to the house last week responding to adverse finding in the FWA report.

Even if there were grounds, it would be up to parliament to terminate the appointment of a member of the FWA tribunal, Justice Ross said.

Mr Thomson's allegations that Terry Nassios, the FWA officer in charge of the investigation was "selective and biased", should be tested in the Federal Court.

"These are serious allegations, made against a career public servant," Justice Ross said.

"Any allegations of bias can be tested in those proceedings."

Mr Thomson said FWA had not outright denied his claim its report was selective and biased.

"Justice Ross has not denied that the FWA report into the HSU national office was selective and biased," Mr Thomson told AAP.

But Justice Ross did acknowledge the time it took for the investigation, which began in 2009, was "unreasonably" long and had damaged the body's reputation.

Liberal frontbencher Eric Abetz, who questioned FWA officials at the hearing, said the evidence given at Monday's inquiry should be considered by the privileges committee, which is already investigating whether Mr Thomson misled parliament.

"We've had confirmation that the suggestion of phone hacking was only put to Fair Work Australia after they sent draft findings to him (Mr Thomson) and the Labor-funded lawyers then sent in that submission," Senator Abetz told reporters in Canberra.

"Further we heard from Fair Work Australia the allegations against two senior officers have been completely and utterly dismissed.

"So we had all these straw men that were served up to us and this government authority ... absolutely blowing Mr Thomson's cover."

Meanwhile, FWA acting director Ailsa Carruthers said Mr Thomson's claim under privilege he was threatened by union rivals that he would be set up with hookers to ruin his political aspirations were only raised with the authority in March.

The claim was made in a letter from Holding Redlich lawyers, which until recently were funded by NSW Labor to defend Mr Thomson.

Both Mr Lawler and Mr Nassios are both on extended leave from FWA.

Senator Abetz said it was "not ideal" that Mr Nassios could not be questioned about his report until next year.