Oscar winner Geoffrey Rush has stepped down as president of Australia's screen industry academy after a theatre company revealed it had received a complaint against him for "inappropriate behaviour".

Key points: Geoffrey Rush steps aside as president of AACTA

Geoffrey Rush steps aside as president of AACTA Rush denies any inappropriate behaviour at Sydney Theatre Company

Rush denies any inappropriate behaviour at Sydney Theatre Company Actor says decision "to clear the air is the best for all concerned"

Rush has denied any inappropriate behaviour at the Sydney Theatre Company.

Media reports said the allegation dated from Rush's starring role in King Lear two years ago.

Rush announced on Saturday he was stepping down as president of the Australian Academy of Cinema and Television Arts (AACTA) ahead of the academy's annual awards on Wednesday.

Rush said in a statement to The Associated Press he was stepping down "effective immediately and until these issues have been resolved".

AACTA said in a statement it accepted and respected Rush's decision to voluntarily step aside as president.

"We have been deeply concerned about the situation and support a course of action that both respects Geoffrey's rights to the presumption of innocence and due process, but also acknowledges good corporate governance in these circumstances," the statement said.

"We will not be making any further comment at this time."

Rush said in his statement he did not want professional colleagues associated with any allegations.

"Certain recent media reports have made untenable allegations concerning my standing in the entertainment community," said through his lawyer Nicholas Pullen.

"It is unreasonable that my professional colleagues should be somehow associated with such allegations.

"In the circumstances, I have decided to step aside in my ambassadorial role as president of AACTA effective immediately and until these issues have been resolved.

"This decision has not been made lightly. However, in the current climate of innuendo and unjustifiable reporting, I believe the decision to make a clean break to clear the air is the best for all concerned."

Geoffrey Rush has won the "Triple Crown of Acting". ( AAP: Tracey Nearmy )

The Sydney Theatre Company has not disclosed details of the allegation. It said the complainant requested that the allegation be dealt with confidentially, and did not want Rush notified or involved in any investigation.

Rush has performed at the Sydney theatre for 35 years.

The company said the complaint was made after Rush's employment had ended and it disclosed it when a journalist asked in early November.

The company did not say what action it had taken and it did not respond to questions about whether it would work with Rush in the future.

Rush's lawyers said his "regard, actions and treatment of all the people he has worked with has been impeccable beyond reproach".

The actor said on Thursday he became aware of "rumours of a complaint" but the theatre had refused to provide details at the time.

His lawyer said Rush "abhorred any form of maltreatment of any person".

"Until there is the decency afforded to Mr Rush of what the 'inappropriate behaviour' actually is then there is nothing more that can be said at this stage," Mr Pullen said.

"The public and the media need to note this is a highly stressful and frustrating time for Mr Rush and his family, especially when there are no details concerning the 'inappropriate behaviour'."

Rush is one of Australia's most respected actors and among the few who have won the "Triple Crown of Acting", meaning he has won an Academy Award, Primetime Emmy Award and a Tony Award.

The 66-year-old won the 1997 best actor Academy Award for Shine and has three other Oscar nominations. He is perhaps best known as Captain Barbossa in the Pirates of the Caribbean films.

AAP/AP