The federal government is expecting more institutions to join the $3.8 billion national redress scheme for child sexual abuse survivors in coming weeks.
Legislation to establish the scheme cleared parliament on Tuesday, with victims able to apply for redress from July 1.
Every state and territory government has committed to the scheme, along with the Catholic Church, the Anglican Church, the Salvation Army, the Scouts, the Uniting Church and the YMCA.
"That takes coverage to over 90 per cent and I look forward to other institutions joining over the coming weeks," Social Services Minister Dan Tehan told parliament.
Labor, the Greens and independent Derryn Hinch have raised concerns the maximum payment is $150,000 rather than the $200,000 recommended by the child abuse royal commission.
The government argued while the cap was lower than what the commission recommended, the $76,000 average payment is $11,000 higher.
Survivors will also be able to access psychological counselling services and personal apologies from institutions.
Labor and the Greens raised additional concerns over the availability of counselling services and the indexation of past pay-outs.
Greens senator Rachel Siewert said there was uncertainty over whether psychological services would be available to survivors for the whole of their lives.
"We share concerns with survivors that the scheme is not the best it can be given there are some issues that remain unresolved," Senator Siewert said.
Law Council of Australia president Morry Bailes said the scheme was important in acknowledging Australia and institutions failed to protect many children from child sexual abuse.
"The scheme provides an opportunity to respond to these past wrongs and provide survivors with access to a just response," Mr Bailes said.
