Bovell, who will address the National Play Festival on Thursday, said: ''I go to London and I see actors from a Caribbean background or subcontinent background playing roles from their own cultural stories and playing roles in Shakespeare, Ibsen and Chekhov.

''It is something Australia is still not addressing. We have to identify [racism's] roots and we have to take responsibility both in terms of the indigenous question - something that really matters to me - and to the question of asylum seekers.''

In his speech, Bovell will speak about racism and its historical roots in Australia and ask why, after more than three decades of debate, the stages are still dominated by Anglo-Australian stories and actors. He believes it stems from long-standing institutionalised racism.

''I don't think we should be talking about what kind of theatre we should or shouldn't have, but what kind of society we want and how can theatre contribute to the process of defining what that could be,'' said Bovell, whose adaptation of Kate Grenville's The Secret River last year won six Helpmann Awards.

Performers' union Actors Equity set up a diversity committee last year to promote and advocate for more diverse casting. One member, Asian-Australian actress Pearl Tan, said they were working with a researcher at Macquarie University to look at the breakdown of their membership base compared with the census, and with what was happening on stage and the screen.

The National Play Festival, which is run by Playwriting Australia in association with Carriageworks, will present several public readings of new plays, many with a focus on diversity. Tan will star in two, including Moths by Asian-Australian playwright Michele Lee, in which six actors explore gender and Asian identity.

Tan said you could put a whole cast of white people on stage and nobody would notice, ''but if you come to a play and there are six Asian-Australians on stage, then it's a political statement''.

Moths playwright Lee agreed that theatre in Australia was ''very white''. ''When it's not white, it's community theatre,'' she said.

Rachael Maza, artistic director of Melbourne's Ilbijerri indigenous theatre company, said: ''Without question we all live in this idea that we are still a White Australia, and there is no question this is still being perpetuated and reflected in that art that's being made.''

Maza, who began her career as an actress, said indigenous actors were generally cast in roles not written specifically as indigenous, only when a director or producer wanted to make a statement. ''I know for a fact that every young black actor who comes out of acting school is probably going to … quickly realise they're going to get indigenous roles or occasionally the odd role where the director or producer is being wild.''

However, she also said there had been a shift in the last decade, with companies wanting to collaborate to tell indigenous stories.

The National Play Festival is at Carriageworks from June 12 to 15.