The church's Truth, Justice and Healing Council – a national mouthpiece established after the royal commission was announced – issued a statement on Thursday, saying that it would ask the attorneys-general of the federal, state and territory governments to begin working on the scheme.
The move comes a day after a state committee tabled its Betrayal of Trust report, the result of an 18-month inquiry into the handling of child abuse by religious and other organisations.
Georgie Crozier, the chairwoman of the inquiry's committee, delivered the report to parliament with a slew of stinging rebukes of the Catholic Church's leaders, whom she accused of trivialising the problem of child abuse as a "short-term embarrassment".
The Council's chief executive, Francis Sullivan, said federal, state, and territory governments should consider extending the state inquiry's proposed scheme nationally, and that it should have consistent investigative powers and payments.
“A national compensation scheme, funded by the church and other organisations and with no caps on payments, is an important first step in taking away from institutions such as the Catholic Church the role of investigating complaints and determining compensation for victims," he said.
This departs from the church's traditional position to argue that its internal processes were proof that its approach to abuse had improved over time.
The Catholic Church's Melbourne Response scheme currently places a $75,000 cap on victims' compensation claims in Victoria, while its national equivalent, Towards Healing, is unlimited.
In Good Faith & Associates' director Helen Last has said that the church had settled thousands of claims outside of Melbourne Response, in an attempt to silence them.
Mr Francis said the state inquiry's recommendation, coupled with the royal commission's potential to do the same, should be enough for governments to consider a national approach to child sexual abuse and child protection.
He said: “We will also call on all governments to start working towards a national approach to uniform police reporting requirements and statutory complaint handling processes."