The Daily Telegraph's publisher has abandoned a claim midway through an appeal hearing that the judge in the Geoffrey Rush defamation case acted in a way that made him appear to be biased.

Rush, 68, successfully sued Nationwide News and journalist Jonathon Moran over two front-page stories and a newsagent poster published in late 2017, which detailed allegations that he behaved inappropriately towards a co-star during a Sydney Theatre Company production of King Lear in 2015-16.

The stories did not name the woman at the centre of the allegation, who was later revealed to be actor Eryn Jean Norvill. She did not co-operate with the stories but later agreed to give evidence in court.

Earlier this year Federal Court Justice Michael Wigney found Rush was defamed and awarded him $850,000 in damages plus $1.98 million for past and future economic loss.