Oscar-winning actor Geoffrey Rush is suing News Corp's Sydney masthead The Daily Telegraph over a series of allegations the publication has run in the past week.

Speaking at a press conference in Melbourne, the Pirates of the Caribbean star described claims made by the publication as "slurs" and "hyperbole". 

"The Daily Telegraph has made false, pejorative and demeaning claims, splattering them with unrelenting bombasity on its front pages," he said.

"This has created irreparable damage to my reputation [and] been extremely hurtful to my wife, my daughter and my son. The situation is intolerable and I must now seek vindication of my good name through the courts."

Last Thursday, The Daily Telegraph ran a "world exclusive" on its front page revealing the Sydney Theatre Company had received a complaint about Rush's behaviour during 2015's production of King Lear.

The tabloid did not detail the specifics of the complaint and the former King Lear colleague did not speak on the record. The story quickly made headlines around the world, with Rush strongly denying any wrongdoing. 

Since the news first broke, the Telegraph has covered the story in print at least nine times. Melbourne's Herald Sun has only run the story in its print edition twice. 

Last week, Herald Sun journalists were told not to tweet the Telegraph's story because it was "highly libellous". Fairfax Media understands the original story was due to appear on the Melbourne paper's front page, but was dropped shortly before the newspaper was sent to print.

Rush's lawyer, Nicholas Pullen from HWL Ebsworth, confirmed the proceedings were only against The Daily Telegraph and that his client was seeking damages.

He would not say whether he has requested the Daily Telegraph take the story down. 

"The normal process in these type of proceedings is damages," he said. 

Mr Rush declined to answer questions. 

Rush has been defended by several people in the Australian arts world, including theatre director Neil Armfield and Rachel Griffiths.

"Geoffrey Rush is not Harvey Weinstein," the actress said at this week's AACTAs. 

Melbourne Theatre Company has said it is "monitoring" the Rush allegation ahead of the 2018 run of Shakespeare's Twelfth Night. It has confirmed it has not received any complaints about the Oscar-winning actor's behaviour on or off the stage. 

In September, fellow Australian performer Rebel Wilson was awarded $4.56 million after successfully suing Bauer Media over a series of defamatory articles. However, the magazine giant has turned to the Court of Appeal in the hope of reducing the multimillion dollar payout.