The 66-year-old denied any wrongdoing after Sydney's Daily Telegraph ran a front-page story last month reporting that the Sydney Theatre Company received a complaint about him when he was working with them.
The allegations of inappropriate behaviour date back to a Sydney Theatre Company production of King Lear in 2015 and 2016. The theatre company said it complied "in the interest of the complainant's health and welfare".
"Today I filed defamation proceedings in the federal court of Australia against the Daily Telegraph", he said at a brief press conference in Melbourne.
The newspaper, owned by News Corp Australia, ran allegations against Rush that he called hyperbolic and untrue.
On Friday, Rush said the Daily Telegraph had 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.
"The situation is intolerable and I must seek vindication of my good name through the courts".
Australia is now home to the world's first blockchain-based stock exchange
The system, which was developed by Digital Asset (DA), will replace the Clearing House Electronic Subregister System (CHESS ). The ASX said it would release details on how the system would work and when it might be launched in March next year.
Rush said he would not be answering any further questions beyond his statement made to a packed room of journalists and flashing cameras at his lawyers office on Collins Street.
The Daily Telegraph editor Chris Dore says his newspaper had accurately reported that the theatre had received the complaint.
The actor resigned the president of the Australian Academy of Cinema and Television Arts Awards after the allegations emerged and missed this week's awards ceremony.
Rush's lawyer Nicholas Pullen said police had not been in contact with his client over the allegations.
Rush won the Academy Award for Best Actor for the 1996 film Shine, in which he played celebrated concert pianist David Helfgott.
The Daily Telegraph has yet to issue comment on the legal proceedings.
There's no court date as yet, but we'll keep you posted.