NSW Education Minister Rob Stokes also dismissed the plan which will see the Morrison government create a special $1.2 billion fund for private schools and pay it directly to Catholic and independent school authorities to distribute as they see fit.

The “choice and accessibility fund” is in addition to a separate $3.4 billion cash injection announced last Thursday by Prime Minister Scott Morrison to help private schools adjust to a new model for determining socioeconomic disadvantage.

“We are the Gonski State,” Mr Stokes said in a statement. “Quite simply, I won't be signing any deal that doesn't treat every student and every school with fairness.”

NSWTF Illawarra organiser John Black said the new “funding deal fails to provide a single additional dollar for students in public schools”.

Mr Black said the Coalition’s $4.6 billion increase to private school funding was a cynical attempt to buy votes ahead of the next federal election.

“It is totally unacceptable to fund private schools while failing to meet the needs of the public school students,” he said.

“When Rob Stokes says this funding deal is grossly unfair to public school students, Scott Morrison ought to be taking notice.”

Read more: Fight against $1.9 billion school funding cuts to hit Illawarra streets

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

Government documents indicated the new $1.2 billion pot of money will be used for “government priorities for school education”, including regional, rural, remote and drought-affected schools.

Labor's education spokeswoman Tanya Plibersek and former NSW education minister Adrian Piccoli, a National, both dubbed the pot of money a “slush fund”.

The Catholic and independent school sectors cautiously welcomed Thursday's announcement, but left the door open to future arguments over funding.