An education funding expert says alleged donations by Catholic Schools NSW to the Liberal party, under investigation by the state corruption watchdog, show governments need to check taxpayer funding was “being spent according to its purposes” and not funnelled into political donations.

The Independent Commission Against Corruption (Icac) is investigating allegations that political donations were made by Catholic Schools NSW “in amounts that were not declared and exceeded applicable donation caps”.

It is alleged the donations were arranged and approved by the Catholic Schools NSW chief executive, Dallas McInerney, to recruit or renew members to the party – a practice known as “branch stacking”. Catholic Schools NSW is the governing body for nearly 600 schools.

Trevor Cobbold, the convenor of the advocacy group Save our Schools and a former Productivity Commission economist, said the commonwealth and state governments should act alongside the Icac investigation “in the face of very serious allegations” to jointly audit Catholic Schools NSW.

Cobbold said nearly 80% of funding for Catholic schools comes from federal and state funding, or around $3.8bn in 2024. As a registered charity with the Australian Charities and Not-for-profits Commission (ACNC), it would be at risk of losing its charitable status and tax exemptions if it is found to have a “disqualifying political purpose”.

“The commonwealth department of education, the federal minister for education, and the New South Wales minister for education can’t stand aside as if they are uninterested observers,” Cobbold said.

“They have specific responsibilities that are not those of Icac … to ensure that public money is being spent according to its purposes and in order to do that they need to have a joint audit of the books of Catholic Schools NSW.”

“It does raise broader issues about how school organisations account for taxpayer funding.”

Chris Bonnor, a former president of the NSW Secondary Principals Council and the author of Waiting for Gonski: How Australia failed its schools, said the allegations “call for much more stringent monitoring of compliance” by private schools with regulations.

“Along with unequal obligations on the public and private sector, there’s been unequal regulations and unequal accountabilities”.

On Tuesday, Chris Minns said his government would wait for the Icac investigation to begin, but ruled out an immediate audit of Catholic Schools NSW.

“We don’t have any plans to do it … I think we should wait for that to at least begin,” the NSW premier said in Sydney. “I think we should wait for it to report both to parliament and other independent bodies.

A spokesperson for the NSW Liberal leader, Kellie Sloane, declined to comment on Tuesday.

Sloane, when previously asked about the possibility of public funds being used in alleged donations, said “no stone should be left unturned”.

“But these are very serious allegations, and I trust the Icac to do its work,” she told reporters earlier this month.

The NSW Greens have called for a separate audit of Catholic Schools NSW and renewed their push to stop public funding of private schools.

“The idea that public funds going to Catholic schools and being misused and misappropriated is outrageous. Any school that is alleged to have engaged in corrupt conduct should have all public funds denied until the investigation is conducted,” said Tamara Smith, the NSW Greens education spokesperson.

In separate statements to Guardian Australia, the federal education department and the NSW Education Standards Authority (NESA) refused to comment on the allegations.

A spokesperson for NESA said “as these matters are the subject of an active Icac investigation we are unable to comment”.

In a statement, the ACNC said it was aware of Icac’s “investigation of claims in relation to Catholic Schools NSW Limited”. “The ACNC will monitor the ongoing ICAC investigation,” it said.

Cobbold argued two inquiries into the allegations could run concurrently, and pointed to the royal commission into antisemitism and social cohesion taking place at the same time as the criminal investigation of the Bondi terror attack.

“Inquiries in the past, take the royal commission, they can overlap. One organisation is meeting its legal responsibilities and the other organisation should be meeting theirs, and by that I mean the NSW and commonwealth governments … and the charities commission,” he said.

The Icac probe is part of a wider investigation of allegations against individuals connected to the Liberal party including McInerney, property developer Jean Nassif, and two brothers of the former Liberal premier Dominic Perrottet, Jean-Claude and Charles, who all have previously denied wrongdoing. Perrottet is not accused of any wrongdoing.

McInerney was appointed as the inaugural chief executive of Catholic Schools NSW in 2017. The former member of the Liberal state executive is a factional ally of the federal Liberal leader, Angus Taylor, who is not accused of any wrongdoing.

In a statement reported by the Sydney Morning Herald on 2 July, McInerney said he had offered to stand aside “to allow the work of Catholic Schools NSW to continue its important mission”. Catholic Schools NSW has been contacted for comment.