In a short statement to media today, Rush described the allegations as "slurs, innuendo and hyperbole", and said they had caused "irreparable damage" to his reputation, as well as hurt to his family.
"The Daily Telegraph have made false pejorative and demeaning claims splattering them with unrelenting bombast on its front pages".
"I must now seek vindication of my good name through the courts", Rush said.
The complaint was made after the play had ended in January 2016, but no details have been published.
"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", a letter from his lawyer to media read. "It is unreasonable that my professional colleagues should be somehow associated with such allegations". A court date is yet to be set.
The Daily Telegraph's editor Christopher Dore said: "The Daily Telegraph accurately reported the Sydney Theatre Company received a complaint alleging that Mr Geoffrey Rush had engaged in inappropriate behaviour".
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Comment was being sought from the Daily Telegraph.
The actor resigned from his role as president of the Australian Academy of Cinema and Television Arts (AACTA) in the wake of the printed story and did not attend the body's awards last week.
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.
Rush is one of Australia's most respected exports, starring in acclaimed films like Shakespeare in Love , Elizabeth and The King's Speech.
Rush's solicitor, Nicholas Pullen, stated that the court documents had only been filed with the Federal Court of Australia earlier today, and that this press conference would likely be the first anyone at the Daily Telegraph would've heard of them.
"This is an action against only the Daily Telegraph", he said.
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