Rush told media he has filed defamation proceedings against the Sydney paper The Daily Telegraph. "They have splashed spurious claims with bombastic titles on their front pages", the Oscar-winning actor said in a brief press conference in Melbourne.
He said the claims had "created irreparable damage" and was "extremely hurtful" to his family and colleagues in the industry.
"The situation is intolerable and I must seek vindication of my good name through the courts", he said.
The Daily Telegraph on Monday published the allegation which dates back to a performance of King Lear from 2015, allegations which Rush vigorously denied in a series of statements through his lawyers saying he had not been informed by the STC of the existence, or the nature, of the complaint.
The newspaper said it would defend its reporting.
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"We will defend our position in court". The company has released no details of the complaint other than it alleged "inappropriate behaviour" while Rush was an employee and was not raised until after he had left.
The anonymous person also made a complaint to the STC but insisted it remain confidential and that Rush was not notified of it.
When asked about the claims being leveled against Rush, Australian actress Rachel Griffiths said the actor "is not Harvey Weinstein" - referencing the Hollywood mogul who faces multiple allegations of sexual misconduct.
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.
The actor is best known for his movie roles in Shine, the Pirates of the Caribbean films, The King's Speech and Shakespeare in Love.