CANBERRA, May 7 - Catholic education authorities estimate fees at Sydney schools could rise by $5000 over the next five years, and $4000 in Melbourne, News Corp reported on Sunday.

But the government says its new funding plans are fair and will lead to Catholic schools getting an extra $1.2 billion by 2021.

Treasurer Scott Morrison said he would always argue for fairness.

"We can't walk away from the principle which says that every child's funding for their schooling should be based on a clear standard," he told the Nine Network on Sunday.

"There shouldn't be special deals, there should be one deal."

Education Minister Simon Birmingham said the modelling showing large hikes in Catholic school fees was fundamentally flawed.

"I am committed to stopping the school funding wars and I urge all parties to end their scare tactics and stop their campaigns for special treatment," he said.

The government's stance has won support from the Greens, with the minor party's education spokeswoman Sarah Hanson-Young saying Catholic authorities had to be up front with parents.

"There are very serious allegations that the Catholic schools commission have been funnelling money away from poorer schools and pouring it into richer schools," she told reporters in Canberra.

"I think there are some people within the schools sector who are more worried about the transparency measures outlined in this package than they are about the actual money going in."

Labor is siding with Catholic educators, saying it trusts what the school systems say over the government.

Shadow treasurer Chris Bowen says Catholic schools would be in meltdown by the end of the decade and there was a breakdown in trust between the sector and the government.

"Their one-size-fits-all model will have very significant ramifications for the 20 per cent of Australian students educated in the Catholic system," he told ABC TV.

The government plans to boost its share of funding from $17.5 billion in 2017 to $30.6 billion by 2027, with the aim to bring all schools to the same level per student once state government cash is added.

Its funding formula takes into account the socio-economic status of a school community, with those where parents are less likely to be able to pay higher fees slated for more government money.