One reporter asked if Rush had sought a retraction or apology from the Daily Telegraph.
The stories accused rush of misconduct during his time at the Sydney Theatre Company during a production of King Lear in 2015 and 2016.
"Mr Rush has not been approached by the Sydney Theatre Company and the alleged complainant nor any representative of either of them concerning the matter you have raised", the letter stated. It did not specify the name of the complainant or details of the complaint.
The actor said he would be taking legal action against The Daily Telegraph for publishing reports about the claims, which he dubbed "false", "demeaning", and "intolerable".
This has created irreparable damage to my reputation has been extremely hurtful to my wife, my daughter and my son and to my extended family as well as to many colleagues in the film televisions and theatre industry.
Australian actor Geoffrey Rush will sue the Daily Telegraph newspaper for allegations published about his behaviour with a fellow actor on stage.
The 66-year-old actor did not take questions from the media today.
Rush's lawyer Nicholas Pullen did not specify the damages Rush is seeking.
Soon after the allegations were reported, Rush stepped down as the president of the Australian Academy of Cinema and Television Arts Awards, just days before the organisation's seventh ceremony.
He has previously said that he had not been informed of the existence or nature of any complaint.
Australian actor Geoffrey Rush has faced the media for the first time since allegations of "inappropriate behaviour" were made against him.Rush says he had filed defamation proceedings against News Corp paper the Daily Telegraph.More: https://yhoo.it/2BehdB1Report on 7 News at 6pm.
The publisher has since said it would appeal the payout as the "unprecedented" amount had major implications for the media industry.
"We don't have our have a trial date yet, this has only been set up this afternoon".