"It's clear that he should resign and I think it's time has come now for the ultimate authority in the church to take action and sack him."

In May Wilson was found guilty of concealing the sexual abuse of children between 2004 and 2006 at the hands of paedophile priest Jim Fletcher in the 1970s.

It can be revealed that Mr Turnbull took action behind the scenes to have Wilson sacked after the 67-year-old was sentenced on July 3 to 12 months' detention.

Australia's ambassador to the Vatican and the Holy See, Melissa Hitchman, was instructed to make representations to have Wilson sacked.

Mr Turnbull also made his views known to Sydney Archbishop Anthony Fisher and Brisbane Archbishop Mark Coleridge.

The Prime MInister's comments on Thursday came before he met a delegation of archbishops Anthony Fisher and Mark Coleridge and Melbourne Archbishop-elect Peter Comensoli to discuss a range of issues causing friction between the church and the government.

These included Wilson's refusal to step down and a discussion of the recommendations from the Royal Commission into Institutional Responses to Child Sexual Abuse. It was expected to include the church's reluctance to force priests to break the seal of confession to report child abuse.

School funding

The biggest policy issue on the agenda was funding for Catholic schools, which was trimmed last year when the government introduced a revamped model.

Since then, there has been a review of the methodology used to determine each school's socioeconomic status and, hence, funding levels.

The government will adopt the new socioeconomic system that would use a direct measure of parental income to determine a school's ability to contribute to the recurrent costs of the school. This would make the Catholic sector slightly better off.

The current socioeconomic system estimates what people can afford to pay based on their neighbourhood.

Before the meeting, Archbishop Coleridge told The Catholic Leader  there is a "crisis that is looming for Catholic schools around the nation if the current funding model applies".

"We want to work collaboratively to solve what is a problem for both the government and the church – and by implication for the whole country," Archbishop Coleridge said.

Before the government introduced its Gonski 2.0 funding model, which aimed to treat all schools on a needs basis, Catholic sector funding was based on a more generous formula called the "system weighted average", created by Labor in 2013 when it was desperate to win support for its school funding changes.

Under the new policy, funding for Catholic schools will increase by an average of 3.7 per cent a year over the next decade compared with 4.7 per cent for the independent sector. The sector said this would leave it $80 million a year worse off.

To placate the sector, Education Minister Simon Birmingham promised $50 million in transitional assistance for the hardest-hit schools and the SES review.

None of this mollified the Catholic education sector, which vowed to campaign against the Coalition all the way to the next election if need be.