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A survivor-focused reference group will be appointed to advise the government on the form and content of the apology, which Mr Turnbull has promised to deliver by the end of the year.
"We owe it to survivors not to waste this moment and we must continue to be guided by their wishes," he told parliament on Thursday.
"As a nation, we must mark this occasion in a form that reflects the wishes of survivors and that affords them the dignity to which they were entitled as children, but which was denied to them by the very people who were tasked with their care."
Mr Turnbull made the promise while updating colleagues on a redress scheme for survivors, due to be rolled out by July 1 after being recommended by the Royal Commission into Institutional Responses to Child Sexual Abuse which finished up last year.
He urged the states, territories and non-government organisations not to delay signing up, saying only maximum participation would allow the scheme to be successful.
Opposition leader Bill Shorten suggested the government host an event at Parliament House to thank and recognise survivors.