Oscar-winning actor Geoffrey Rush has stepped down as president of Australia’s screen industry academy, days after a theatre company revealed it had received a complaint against him of “inappropriate behaviour”.

Rush has denied any inappropriate behaviour at the Sydney Theatre Company. Media reports this week said the allegation dated from Rush’s starring role in the leading Australian company’s staging of William Shakespeare’s King Lear two years ago.

Rush said on Saturday he stepped down as president of the Australian Academy of Cinema and Television Arts ahead of the academy’s annual televised awards in Sydney on Wednesday.

“Certain recent media reports have made untenable allegations concerning my standing in the entertainment community. It is unreasonable that my professional colleagues should be somehow associated with such allegations,” Rush said in a statement through his lawyer, Nicholas Pullen.

“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.”

Aacta said in a statement it accepted and respected Rush’s decision to voluntarily step aside.

“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,” Aacta said, adding it would not comment further.

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

Rush has performed at the company for 35 years. 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.

Australian media reports say the allegation dated from the company’s production of King Lear from November 2015 to January 2016.

Sydney’s the Daily Telegraph newspaper cited two unnamed theatre sources on Friday that an actor had accused Rush of touching her inappropriately.

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 company had refused to provide details at the time.