Asked about the absence of any new money for public schools,Mr Morrison said public school funding was chiefly the responsibility of state governments.

"I don't think parents will be cynical,"he said."They will note that we're funding public schools at record levels. And all parents want to have choices about how they educate their children."

Funding for private schools is tempered by each school's level of socioeconomic advantage,which is currently assessed based on census data of the school's surrounding geographic area.

Under the new model,a school's SES score will be determined based on the income tax records of its parents,which is possible because of the government's modern data-matching capabilities.

Private schools that are currently overfunded by the Commonwealth - that is,schools which receive more than 80 per cent of their entitlement from Canberra - will get an extra two years to transition down to their fair funding level.

Mr Morrison said the extra money would ensure parents"have choice in education". But shadow education minister Tanya Plibersek rubbished the deal as a"final insult",and said Labor would spend even more on Catholic,independent and public schools.

"We don't believe this restores all of the money that has been cut from Catholic and independent schools,"she said.

"This is still billions of dollars less than all schools would have got under the original arrangements struck by Labor."

The National Catholic Education Commission welcomed the government's changes,signalling an end to the brutal campaign waged against Senator Birmingham's original proposal,led by Victoria.

Acting executive director Ray Collins said the new SES model was"fairer"and went"a long way to fixing problems caused by the model introduced in 2017",but it would need to be reviewed again.

Education Minister Dan Tehan said the new $1.2 billion"choice and affordability fund"would be"sector blind",although it was only for private schools. Mr Morrison said the fund would support schools in regional,rural and remote areas,as well as schools affected by the drought.