State and territory governments will use the commonwealth’s deal with the private school sector to push back against funding commitments for public schools at the heart of the landmark Gonski 2.0 deal.

Last week the federal government announced a $4.6bn deal for the Catholic and independent sectors in a bid to end its long-running feud with them.

But the deal has opened a new front in the funding wars, and prompted state education ministers to argue for concessions from the $23.5bn Gonski 2.0 deal agreed last year with the commonwealth.

The terms of the Gonski agreement required states to lift their overall funding to public schools to at least 75% of the school resource standard by 2023.

That meant a substantial increase in overall funding for a number of states. At the time the federal government released figures which showed that Victoria provided about 66.15% of the SRS, and the Northern Territory, New South Wales, South Australia and Queensland contributed less than 75%.

While most of the states have insisted they will reach that figure, behind the scenes education ministers have been pushing for changes to the way funding is calculated.

Some ministers have argued, for example, that early childhood education, capital spending on school buildings and school transport costs should be included in the overall spend.

The NT’s education minister, Selena Uibo, was “disappointed” the commonwealth “does not recognise the significant NT investment in early childhood as making a contribution to improved education outcomes in the schooling system”.

“We are yet to see any detail about how much of the $4.5bn for Catholic and independent schools would be allocated to the Northern Territory,” she said.

“However, I am concerned this deal erodes equity in the school funding system and that we will end up with a two-tiered system, where students receive more government funding to attend a private school than a public school.

“Our small jurisdiction has limited capacity to match the commonwealth funding for non-government schools with additional funding for our government system due to the greater number of students, combined with our high number of regional and remote schools and higher rates of disadvantage than other states and territories.”

And comments made by the federal education minister, Dan Tehan, this week suggest the NT is not alone in pushing for changes to their overall funding calculation.

On the ABC’s Insiders program on Sunday, Tehan seemed to indicate he was willing to negotiate on the makeup of the funding calculation.

“These are negotiations, so the NSW state government, for instance, want things included in the way their contributions to their state schools are counted, so we’ll have discussions around that,” he said.

“These are more than just about pure dollar figures, these discussions. I’ve had very good constructive discussions with Rob [Stokes]. The bilateral negotiations are very well advanced and I’m very confident we’ll get an outcome.”

Both the NSW and Queensland education ministers – Stokes and Grace Grace – have threatened not to sign up to a long-term school funding agreement unless the government gives “equal treatment” to the public sector.

Stokes said last week he was committed to “needs-based and sector-blind” funding.

But Glenn Savage, a senior education policy lecturer at the University of Western Australia, said it was unlikely the states would refuse to sign up.

“I think it’s largely political posturing and a political tactic to try to drive a particular outcome,” he said.

“The idea the states might reject a change that would give significantly more money to non-government schools is pretty unrealistic. The opposition within the states from the Catholics and independents would be so severe you can’t really imagine a politician winning any votes by doing it.”

Correna Haythorpe, the head of the Australian Education Union, fears that so-called new space might include changes to the way state funding to public schools is calculated.

Haythorpe said she was concerned the commonwealth may use that as a bargaining chip to win support from the states for the deal with the Catholic and independent sectors.

“We need real money in these packages and the states need to cough up their contribution,” she said.

“I don’t think the public would accept the states not contributing their share. They have to genuinely put in their share. It can’t be falsified to look like a higher percentage. The Gonski review was very clear on the mutual obligation between the states and the commonwealth for the funding of our schools.”

The union has pushed states to reject an “inadequate public school funding deal” and has promised to ramp up its Fair Funding Now campaign in 18 marginal seats.

Tehan said he wanted to conclude bilateral funding negotiations with the states “as soon as possible”.

“These negotiations have been conducted in good faith with all states and territories and I want to ensure that continues,” he said. “At the end of the day the states, territories and the commonwealth want what is best for every student, and that is to ensure certainty of funding for 2019.”