Academy award-winning actor Geoffrey Rush resigned as head of an Australian film industry body Saturday after allegations surfaced against him of "inappropriate behaviour".

Rush, who has denied any wrongdoing, stepped down as president of the Australian Academy of Cinema and Television Arts (AACTA), which he had led for several years, the organisation said in a statement.

"AACTA acknowledges the decision today of Geoffrey Rush to voluntarily step aside as president of AACTA and accepts and respects his decision to do so," it said.

"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 added, declining further comment.

Rush, 66, took the step after the Sydney Theatre Company revealed last week that it had received a complaint alleging that the veteran Australian actor had engaged in "inappropriate behaviour" when working with the company.

No further information about the nature of the behaviour or the identity of the person who made the complaint was revealed, but Australian media reports said the allegations related to Rush's time playing King Lear for the company in 2015 and 2016.

In a statement to public broadcaster ABC, Rush said he was unaware of the details of the allegations against him.

"The moment I became aware of rumours of a complaint I immediately phoned and spoke to senior management at the Sydney Theatre Company asking for clarification about the details of the statement. They refused to illuminate me with the details," he said.

Neil Armfield, a theatre and film director who worked with Rush on King Lear, told the ABC he did not believe the allegations.

"It's not correct, there's no basis... I absolutely do not believe it," he was quoted as saying.

Rush's lawyer, Nicholas Pullen, told the broadcaster that it was "a great disappointment" to Rush that the theatre company "has chosen to smear his name and unjustifiably damage his reputation in this way".

Rush won the Best Actor Academy Award in 1997 for his role in "Shine" and is one of the few actors to have also won a primetime Emmy and a Tony Award.

Source: AFP