Academy Award-winning actor Geoffrey Rush has been accused of "inappropriate behaviour" during his work with the Sydney Theatre Company (STC).

Through his lawyers, Rush has vigorously denied the allegations, saying he had not been informed by STC either of the existence of the complaint or the nature of the complaint.

A Sydney Theatre Company spokeswoman said the organisation had "received a complaint alleging that Mr Geoffrey Rush had engaged in inappropriate behaviour".

"The company received the complaint when Mr Rush's engagement with the company had ended," she said.

"The company continues to work with the complainant to minimise the risk of future instances of the alleged behaviour occurring in its workplace.

"At the time the complaint was made, the complainant requested that the matter be dealt with confidentially, and did not want Mr Rush notified or involved in any investigation.

"STC complied, acting in the interest of the complainant's health and welfare.

"STC has at all times been clear that this was an allegation made to (not by) STC and not a conclusion of impropriety."

Rush, 66, most recently performed in the STC production of Shakespeare's King Lear between November 2015 and January 2016.

However, the 2012 Australian of the Year has also been involved in STC productions like The Importance of Being Earnest and The Government Inspector.

"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," Rush said in a statement to the ABC.

"I also asked why this information was being withheld, and why, according to standard theatre practice the issue had not been raised with me during the production via stage management, the director, my fellow actors or anyone at management level.

"However, no response was forthcoming."

'Highly stressful' time for Rush

Rush's lawyer, Nicholas Pullen, said the actor denied being involved in any inappropriate behaviour.

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

"It is a great disappointment to Mr Rush the STC has chosen to smear his name and unjustifiably damage his reputation in this way," Mr Pullen said.

"Not to afford a person their right to know what has been alleged against them, let alone not inform them of it but release such information to the public, is both a denial of natural justice and is not how our society operates."

Prominent Australian theatre and film director Neil Armfield worked with Rush on King Lear and told the ABC from New York that he did not believe the allegation.

"It's not correct, there's no basis ... I absolutely do not believe it," he said.

Director Neil Armfield (R) and Geoffrey Rush have worked together. ( AAP: Tracey Nearmy )

Rush is one of the country'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 actor's 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'."