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In April this year, Justice Michael Wigney found The Daily Telegraph's publisher and journalist Jonathon Moran were reckless regarding the truth when they reported the Oscar-winning actor had been accused of inappropriate behaviour in 2017.
Rush (67) was awarded $A2.8 million ($NZ2.9 million) - the largest defamation payment in Australian history to date.
Nationwide News is appealing the decision on 20 grounds including that Justice Wigney's conduct "gave rise to an apprehension of bias".
In its amended notice of appeal, filed on Friday, the company says this is supported through "repeated references to the Appellants (the Telegraph and Moran) and the matters complained of by Justice Wigney, orally and in written judgments, in derogatory terms, and the tone in which certain of those references were delivered".
Justice Anthony Besanko, via video link in Sydney on Wednesday, ordered that Nationwide News file and serve submissions and an affidavit in support of its application to access audio from the proceedings by June 21.
The case will return to court on July 15.