Prime Minister Tony Abbott says his government has reached a national “no strings attached” needs-based funding agreement for schools.

The federal government has moved to head off concerns over schools funding after promising to return $1.2 billion to the cash pool and give the sector certainty for the next four years.

But Labor says the coalition is offering a “national bandaid” that gives taxpayers no certainty over how their money will be spent.

After insisting last week they would dump Labor’s Gonski school funding system, Prime Minister Tony Abbott and Education Minister Christopher Pyne on Monday announced they had agreement in principle for a “national, fair and needs-based” model.

NSW, Victoria, South Australia, Tasmania and the ACT all signed up to Labor’s model where each student would attract the same base amount of funding with loadings added for disadvantage.

Mr Pyne said there was now “no plan to alter the way that the model will be delivered in the signatory states”.

The government also plans to remove “Canberra command and control” of funding.

It will dump the requirement for schools to have a plan for how they would use the extra money to improve student achievement and teacher quality, as well as new data collection on school performance.

Monday’s agreement includes the $1.2 billion set aside by Labor for the non-signatory states of Queensland, Northern Territory and Western Australia, bringing the total extra federal funding up to $2.8 billion over the next four years.

The government will also honour promises of $55 million for Catholic education commissions and $110 million for the Association of Independent Schools.

The move was widely welcomed, with National Catholic Education Commission chief Ross Fox saying it gave certainty.

However, states that had signed up to Labor’s plan were cautious.

“Given the way Christopher Pyne has conducted himself over the last week, I won’t be entirely satisfied until we’ve got it in writing,” Tasmanian education minister Nick McKim said.

SA Premier Jay Weatherill said his state wanted “every dollar and every cent put back where it belongs”.

Some conditions placed on NSW, Tasmania, South Australia, Victoria and the ACT won’t apply to the other three states.

Labor believes this is likely to include guarantees that states won’t cut school funding.

“When you say no strings attached, that means here’s a wad of cash, do with it what you like,” opposition education spokeswoman Kate Ellis said.

“There are no guarantees for parents or for taxpayers that there is any form of accountability.”

Labor challenged the government to repeat pre-election commitments that no school would be worse off.

But Mr Pyne stopped short, telling parliament “no school is going to be worse off because of anything the commonwealth does”.

At the same time, government minister Eric Abetz told the Senate: “You might actually find some schools are worse off courtesy of … various state government decisions.”

The Australian Education Union said it wasn’t a national agreement because WA, Queensland and NT would get the extra federal funding without having to co-contribute, maintain their spending or distribute the money according to need.

“Kids in the NT, Queensland and WA have been short-changed – the Abbott government hasn’t even bothered to ensure this money gets to schools,” deputy federal president Correna Haythope said.

Mr Abbott said it would be “poor form” for the states to cut their funding.