The Turnbull government has guaranteed a showdown with the Catholic schools sector after Education Minister Simon Birmingham signalled he would not bend to pressure over plans for a new education funding model.

On Thursday Senator Birmingham hit back at claims from the Catholic sector that some schools would be forced to close while others would have to hike fees and sack staff due to the new arrangements.

Senator Birmingham was speaking at the National Press Club when his speech was briefly interrupted by protesters who rushed the stage, threw paper in the minister’s face and chanted “no cuts, no fees, no corporate universities” over separate increases to university fees.

Accusing the Catholic Education Commission of spreading “misrepresentations”, Senator Birmingham said the new funding model would put a stop to different sectors, or state governments, trying to “blackmail or bully federal governments into doing something that suits them”.

“The whole point of the reforms we have announced to school funding is to get away from special deals, to get away from ancient sweetheart arrangements,” he said.

Protesters have interrupted Education Minister Simon Birmingham's National Press Club address. They were removed promptly@abcnews pic.twitter.com/O0zDAoQFnQ

— Kerrin Binnie (@kerrinbinnie) May 4, 2017

Catholic sector funding would grow by $1.2 billion over the next four years, Senator Birmingham said, meaning there was “no reason why fees need to increase at any Catholic systemic school”.

The National Catholic Education Commissioner has expressed anger at the changes, which mean a funding freeze for 353 ‘overfunded’ Catholic and independent schools across the country and cuts to 24 more institutions that receive the most generous treatment.

While the National Commission is seeking more detail from the government about its plans, Victorian Catholic Education Commission head Stephen Elder has already accused the government of “smokescreens and mirrors”.

“Let me tell you, his attitude of ‘take it or leave it, no negotiation’, doesn’t cut it with us,” he said on Thursday.

“Catholic families are going to be worse off under this deal.”

In response, Senator Birmingham seized on a press release from last year in which the Victorian commission welcomed the government’s funding plans, which offered $19 million less than the new package.

Labor has said the government’s new funding model is a ‘$22b cut’. Photo: AAP

“So funding that they welcomed last year, that they said was ‘more than adequate’ last year to keep up with costs, will increase into the future,” he said.

“That, to me, says there is no justification for claims that there may need to be fee increases.”

Former prime minister Tony Abbott has also warned the funding plan will be “vigorously debated” in the Coalition party room next week, amid speculation some MPs are uneasy about the brewing stoush.

The Catholic sector educates one in five Australian children and has previously waged fierce campaigns on schools funding. In 2016, it urged parents against supporting the Greens in some marginal Victorian seats.

While Labor also backed the Catholic sector in its fight with the government, and decried Gonski 2.0 as a $22 billion cut, education spokeswoman Tanya Plibersek would not commit to reinstating the money if Labor won government.

“We’ll have to see at the time of the next election what the exact figure is but we are fully committed to a proper implementation of a needs-based funding system where schools get to their Schooling Resource Standard,” she told Sky News.

Ms Plibersek also confirmed Labor would wave through funding freezes for 353 ‘overfunded’ schools proposed by the government’s new model, describing it as a “deal done”.

“What we’ve said all along is if the government wants to deal with that we will happen support them on that,” she said.