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Things I Know to be True has already opened at the Christchurch theatre and runs until April 17.
A transgender character, Mia, is played by cisgender actor Simon Leary.
Artistic director Dan Pengelly said the court offered its sincere and unreserved apologies for the distress caused by the casting decision.
The play runs until April 17 at the Court - and is being made into a TV series starring Nicole Kidman.
In a post on the theatre's Facebook page, it said: "We appreciate the courage of the artists and members of the community who have communicated with us over this issue, we offer our thanks for reaching out.
"We commit to putting in place measures to ensure this new cast member will be supported, and we are seeking guidance from experts in the trans community."