A royal commission established in 2012 to investigate abuse was contacted by more than 15,000 survivors with claims -- some decades-old -- involving churches, orphanages, sporting clubs, youth groups and schools.
Turnbull told parliament he would consult with survivors before making the apology on behalf of the nation "before the end of the year".
"As a nation, we must mark this occasion in a form that reflects the wishes of survivors and 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," he said.
The royal commission released its final report in December and said more than 4,000 institutions were accused of abuse, with many of them Catholic-managed facilities.
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It made 409 recommendations, which Turnbull said his government was working through, including a national redress scheme that would support survivors with counselling, psychological care and financial payments.
Canberra has budgeted Aus$33.4 million (US$26.1 million) for the scheme, with survivors eligible for payments of up to 150,000 Australian dollars.
"The money does matter. Compensation does help get people, at least, get back on their feet a bit," he told parliament.
"But it's also a tangible admission that the institution was at fault and they should pay for their wrongs."
Survivor advocate Leonie Sheedy of the Care Leavers Network welcomed the proposed apology but said taxpayer-funded organisations that committed or did not investigate abuse, such as orphanages and the police, should also say sorry.