Adelaide Writers' Week has been cancelled and Louise Adler, who on Tuesday morning resigned as director, has described its collapse as a landmark moment and taken aim at those who engage in acts of censorship.

The event was called off after days of furore regarding the decision to cancel a scheduled appearance by Palestinian-Australian author Randa Abdel-Fattah.

The Adelaide Festival board issued an apology to Abdel-Fattah, which the author posted to Instagram to say she rejected.

"It is clear that the board's regret extends to how the message of my cancellation was conveyed, not the decision itself," she said.