The Oscar-winning actor Geoffrey Rush has denied allegations of “inappropriate behaviour” during a Sydney Theatre Company production of King Lear, after the company said it had received a complaint against him.

Rush’s lawyer said in a statement that Rush had not been informed of the nature of the complaint by the complainant or the theatre company, either at the time the complaint was made 21 months ago or since.

“In this current environment, ‘inappropriate behaviour’ may mean abuse, bullying or other forms of reprehensible activity,” the statement said. “These are matters that deserve forthright and objective levels of discussion. It must be made clear from the outset that Mr Rush abhors any form of maltreatment of any person in any form.”

Rush, 66, who lives in Melbourne, said: “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.

“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.”

An STC spokeswoman told Sydney’s the Daily Telegraph, where the claims were first published, that the company had “received a complaint alleging that Mr Geoffrey Rush had engaged in inappropriate behaviour”. She said the complainant had asked for their identity to be withheld.

“The company received the complaint when Mr Rush’s engagement with the company had ended,” she said.

On Thursday an STC spokeswoman said: “Sydney Theatre Company was asked by a News Ltd journalist earlier this month whether it had received a complaint alleging inappropriate behaviour by Mr Rush while he was employed by the company. STC responded truthfully that it had received such a complaint.

“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. As already stated, the Company received the complaint after Mr Rush’s engagement had ended.

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

Rush won an Academy Award for best actor in 1997 for the film Shine and was named Australian of the year in 2012.

He appeared in the STC’s production of King Lear between November 2015 and January 2016 and has worked several times for the company.

On Thursday, the STC’s online page listing of King Lear was taken down.

In their statement, Rush’s lawyers said they understood the complaint was made “over 21 months ago” and that the STC had originally released its statement “some weeks ago”.

Rush’s lawyer said: “To date, Mr Rush or any of his representatives have not received any representations from the STC or the complainant. In other words, there has been no provision of any details, circumstances, allegations or events that can be meaningfully responded to.”

Rush is the president of Aacta, the Australian Academy of Cinema and Television Arts. In November, Aacta released a statement officially rescinding a historic award given to Harvey Weinstein in 2013.

“We recognise our role in working with our members in upholding standards in our industry that we can all be proud of, including the provision of a safe and respectful workplace,” it said.

Rush’s lawyer said: “It is a great disappointment to Mr Rush the STC has chosen to smear his name and unjustifiably damage his reputation in this way. 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.

“At this stage, Mr Rush can only reiterate his statement that he denies having been involved in any ‘inappropriate behaviour’ whatsoever. 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.

“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’.”