The government should run a mandatory compensation scheme for victims of institutional child sex abuse, the Catholic Church says.

But Archbishop Philip Freier, the newly installed Anglican Primate of Australia, said talks were still going on about the best model for a compensation scheme.

He said there were "active discussions" on Tuesday about the issue in the wake of the Victorian parliamentary committee inquiry into child sex abuse.

"I think there were a couple of models that the Victorian policymakers are putting forward so settling on one might be a bit premature for me yet," Archbishop Freier told reporters on Wednesday.

In a submission to the child abuse royal commission, the Catholic Church's Truth Justice and Healing Council called for a mandatory national victims' redress scheme operated by the government.

That proposed scheme would be funded by the institutions that employed the child abuser and provide compensation for past medical expenses, loss of earnings and pain and suffering.

Council chief executive Francis Sullivan said it needed to be non-adversarial, low cost to claimants and provide compassionate and fair compensation for victims.

"The scheme should be built with prime input from victims and open to anyone who has suffered child sexual abuse within any institution in Australia," Mr Sullivan said on Wednesday.

Archbishop Freier said it was important abuse in the Anglican church was recognised and a determination to improve was shown.

The Bishop of Canberra, Stuart Robinson, made an apology on Sunday to victims of sexual abuse in the Canberra and Goulburn diocese.

Archbishop Freier welcomed the apology as another measure to make sure there is repentance for abuse.

"We should be properly sorry for those things and seek to bring amendment into the lives of people where there has been an injury," Archbishop Freier said.

The royal commission will hold two weeks of public hearings in Melbourne, starting on August 18, to look at abuse allegations in the Melbourne archdiocese and the Catholic Church's Melbourne Response complaints handling process.