"The situation is intolerable and I must now seek vindication of my good name through the courts."
Following the statement, Rush did not take questions from reporters. The matter will go before the Federal Court in Sydney on February 8.
In response to Rush's decision, The Daily Telegraph's editor Chris Dore defended the newspaper's decison to publish the story.
"The Daily Telegraph accurately reported the Sydney Theatre Company received a complaint alleging that Mr Geoffrey Rush had engaged in inappropriate behaviour," Dore said.
"We will defend our position in court."
Today's press conference is Rush's first public appearance since the claims were reported.
Following last week's reports of the incident, The Sydney Theatre Company confirmed it received a complaint but would not disclose details of the allegations.
"At the time the complaint was made, the complainant requested that the matter be dealt with confidentially, and did not want Mr Rush notified or involved in any investigation," a statement read. The theatre company said it complied "in the interest of the complainant's health and welfare."
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 was absent from Wednesday's televised event in Sydney, where stars dodged questions from reporters about the allegations.
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.
"Geoffrey Rush is not Harvey Weinstein and I have had more than a handful of interactions with Harvey Weinstein," Griffiths told the ABC on the red carpet.
The veteran actor received acclaim for his breakthrough performance in the 1996 film Shine, which earnt him an Academy Award, Golden Globe and BAFTA.
Rush is one of Australia's most respected exports, starring in acclaimed films like Shakespeare in Love , Elizabeth and The King's Speech.
— with AAP