The Morrison government has given Catholic schools more than 10 times the amount of money needed to maintain "affordable choice" for parents, according to analysis by the Grattan Institute.

Meanwhile, federal Education Minister Dan Tehan has signalled there is room to compromise as he attempts to fend off a major stoush with the NSW Liberal government over school funding.

The Morrison government has committed an extra $4.6 billion to private schools over 10 years. Credit:Alex Ellinghausen

The $4.6 billion injection into private schools announced last week included a $1.2 billion "choice and affordability" fund designed to help Catholic and independent schools keep fees low.

About $718 million is expected to flow to the Catholic sector, with much of that money earmarked for keeping fees low at inner-city primary schools where government funding will decrease under the new "direct income" method of assessing school wealth.