Actor Geoffrey Rush has resigned as president of Australia's screen industry academy amid allegations of "inappropriate behaviour".

The Oscar-winning star made the decision to step aside from his ambassadorial role after the Sydney Theatre Company said it had received a complaint relating to Rush dating back to 2015 when the 66-year-old was performing in King Lear.

The Pirates of the Caribbean actor, denies the allegations of improper conduct.

Explaining his decision to step down, in a statement through his lawyers, he said: "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.

"In the circumstances, I have decided to step aside in my ambassadorial role as president of AACTA (Australian Academy of Cinema and Television Arts) 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."

The AACTA which is due to stage the annual televised awards in Sydney, said it accepted Rush's decision to step down.

"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," it said.

According to Sky News, the claims against the Oscar-winning actor first emerged in a story by Sydney's Daily Telegraph on Thursday.

The publication alleged that an actress had accused Rush of touching her inappropriately but the complainant had requested the matter to be dealt with confidentially.

Rush's lawyers explained that the actor has not been informed of the nature of the complaint, and criticised STC for having chosen to "smear his name and unjustifiably damage his reputation" by informing the press about it.

They dismissed the allegations adding that his "regard, actions and treatment of all the people he has worked with has been impeccable beyond reproach".