The Sydney Theatre Company was not disclosing details of the allegations, which reports said dated from Rush's starring role in the theater's staging of "King Lear" two years ago.
"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," a statement said. The theater company said it complied "in the interest of the complainant's health and welfare."
HWL Ebsworth Lawyers did not respond to a request for comment Friday, but had issued an earlier statement denying Rush was involved in any inappropriate behavior.
"It is with great disappointment to Mr. Rush the STC has chosen to smear his name and unjustifiably damage his reputation in this way," Thursday's statement said.
Rush has performed at the Sydney theater for 35 years. The 66-year-old Australian actor 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 theater's production of William Shakespeare's "King Lear" from November 2015 to January 2016.
Sydney's The Daily Telegraph cited two unnamed theater sources in reporting Friday that an actress had accused Rush of touching her inappropriately. The sources told the newspaper the theater wouldn't work with Rush again.
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 had said Thursday he became aware of "rumors of a complaint" but the theater had refused to provide details at the time.
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