Justice Michael Wigney in April found the Daily Telegraph's publisher, Nationwide News, and journalist Jonathon Moran were reckless regarding the truth when they reported Rush had been accused of inappropriate behaviour during a Sydney theatre production of King Lear.

The judge said a poster and two articles contained several defamatory meanings - including that Rush was a pervert and a sexual predator - but the publisher hadn't proven they were true.

Justice Wigney previously awarded the Oscar winner $850,000 in damages plus $42,300 interest for non-economic loss but he wanted to further consider other damages and costs.

Following an agreement between the parties, the judge on Thursday awarded Rush a further $1.98 million for past and future lost earnings.

It came after Rush's barrister, Sue Chrysanthou, revealed the actor had offered in early 2018 to settle the case in exchange for an apology and $50,000 plus costs.

She said Nationwide News didn't respond.

The Telegraph and Moran instead tried to prove a truth defence at trial, based largely on the evidence of Rush's former co-star Eryn Jean Norvill, who didn't participate in the articles.

She alleged Rush sexually harassed her during the Sydney Theatre Company's King Lear production in 2015-16 when she played the daughter of his titular character.

Justice Wigney ultimately said Norvill was at times "prone to exaggeration and embellishment" and he wasn't persuaded she was an entirely credible witness. Norvill later said she stood by her testimony.

The judge said Rush had suffered a financial loss as a result of the publications but the prospect he'd never work again was "very remote".

"I consider that, all other things being equal, once his reputation is vindicated, he will eventually be able to engage in acting again," the judge said.

Nationwide News and Moran are appealing Justice Wigney's defamation decision arguing his conduct "gave rise to an apprehension of bias".

They failed on Thursday to have the judge recuse himself from considering an injunction application by Rush which, if granted, would prevent Nationwide News from repeating the imputations it was found to have conveyed.

The publisher's barrister, Tom Blackburn SC, said the proposed injunctions would have a "chilling effect" on discussion of the case. He said Rush was trying to shut down criticism of the judgment.

But Ms Chrysanthou argued any free speech issue was diminished by the narrow range of the orders sought and the "failure by these respondents to justify any of these allegations".

Justice Wigney has reserved his decision on the proposed injunctions.

Australian Associated Press