A now deleted news report in Australia's Daily Telegraph stated that Sydney Theatre Company received a complaint against the Oscar-winner, who starred in the company's adaptation of King Lear in 2015, of misconduct.
According to the Hollywood Reporter, Rush's lawyers, in multiple statements, said, "In this current environment, 'inappropriate behaviour' may mean abuse, bullying or other forms of reprehensible activity.
"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," they added.
"In the circumstances, if such a statement has been issued by the STC it is both irresponsible and highly damaging to say the least.
"Your 'understanding' of what has occurred is, with the greatest respect, simply fishing and unfounded. It does not warrant comment except that it is false and untrue," the statement read.