Government schools will not be eligible for $10m in new education funding announced in Thursday’s drought package, prompting the teachers’ union to argue the measure is elitist and unfair.

The Australian Education Union’s president, Correna Haythorpe, said it was “another slush fund for private schools” on top of the $1.2bn Choice and Affordability fund for Catholic and independent schools, which also included money for drought-affected areas.

On Thursday the education minister, Dan Tehan, announced the Coalition would provide “$10m for schools that are impacted by drought so that they can provide relief to families” – modelled on its response to the Queensland floods – and an extra $5m for childcare centres.

He said the funding would address “the impact on parents of drought and worrying whether they’ll … be able to continue to afford to send their children to school” and the toil and hardship parents suffer paying school fees.

The education department has specified the $10m is only for non-government schools as a “supplementary financial source for schools” which have “introduced fee relief and/or curtailed their operations to cope with this drastic situation”.

Haythorpe told Guardian Australia the measure was “disgraceful” and further evidence the Morrison government only considers the needs of non-government schools.

“We have thousands of government schools – more than 80% of students in rural and remote areas are in public schools and they are deeply impacted by drought,” she said.

It was an “elitist argument” that only parents in non-government schools needed fee relief which “relied on the stereotype that farmers all send their kids to boarding and private schools”.

“To privilege one sector over another is to further entrench a level of inequality,” she said. “If you recognise there is a genuine need, surely you would deliver funding to all sectors [and] not make the package elitist and exclusive?”

Labor’s education spokeswoman, Tanya Pliberksek, said it was “terrific that schools will get some extra help during the drought” but said: “What about public schools?

“Public schools students and parents are struggling through this terrible drought, too. What is Scott Morrison going to do to help them?”