The Telegraph first published the allegations on November 30, which allegedly occurred during a 2015 production of King Lear.
"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.
VETERAN Australian actor Geoffrey Rush has broken his silence on the allegations of inappropriate behaviour being made against him, dubbing the claims "intolerable" and announcing he's filed a defamation lawsuit.
"The Daily Telegraph have made false pejorative and demeaning claims splattering them with unrelenting bombast on its front pages".
The allegations have come after a string of high profile sexual abuse complaints against entertainment industry heavyweights such as Harvey Weinstien, Kevin Spacey and Matt Lauer.
Geoffrey Rush is taking the Daily Telegraph to court for defamation, following a story that was published regarding his time at the Sydney Theatre Company and claims of "inappropriate behaviour".
"I must now seek vindication of my good name through the courts", Rush said.
Rush stepped down from his role as President of the Australian Academy of Cinema and Television Arts on Saturday in the wake of the report.
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The Daily Telegraph editor Chris Dore said they would be defending the newspaper's reporting in court.
He declined to take questions.
No details were provided of the nature of the complaint, and Rush denied any inappropriate behaviour.
Rush said his wife, daughter and son had also been hurt by the allegations.
The Australian actor is a stalwart of Australian theatre, won the 1997 best actor Academy Award for Shine, and has three other Oscar nominations.
He's went on to become one of Australia's biggest and most respected Hollywood exports, starring in Shakespeare in Love, Elizabeth and The King's Speech.
The Daily Telegraph is owned by News Corporation, the publisher of this website.