The federal government has backed down on schools funding after a row with a majority of the states and territories.

It will now provide funding of $2.8 billion over four years to all the states and territories, after deciding to bring back $1.2 billion put into consolidated revenue by the former Labor government.

Prime Minister Tony Abbott said the coalition had secured an in-principle agreement with Queensland, Northern Territory and Western Australia that would allow a national funding system to operate.

“Given that we now have a fair and national deal, the government will put the $1.2 billion that Labor took out back into schools funding over the next four years,” he told reporters in Canberra on Monday.

“There will be full funding certainty over the next four years.”

Last week, the coalition raised the ire of states that had sealed deals with the former government under the so-called Gonski system.

It announced it would only honour agreements for the 2014 school year and review the system for 2015.

NSW, Victoria, South Australia, Tasmania and the ACT were angered that they would miss out on what was promised.

Queensland, Western Australia and the Northern Territory had held out on doing any deals with Labor, but will now get the $1.2 billion earmarked by Labor for their funding.

The Abbott government is also to honour funding promised to non-government representative bodies for four years including $55 million to Catholic Education Commissions and $110 million to the Association of Independent Schools.

Mr Abbott said the decision meant the government was “more than keeping our commitments”.

“We want to keep our commitments in spirit as well as in letter,” he said.

Funding for the Gonski signatory states would be distributed in the same way as previously planned.

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

“I suspect that New South Wales and Victoria will be happy to lose the Canberra command and control elements of those deals but certainly the financial arrangements for the next four years will be absolutely adhered to,” Mr Abbott said.

The government is to shelve Labor’s ideas of imposing management plans for states’ schools systems, setting up Canberra-based inspectors and gathering extra data in Canberra.

Education Minister Christopher Pyne said the government would amend the Australian Education Act in 2014 to “dismantle the regulation and red tape that made the model virtually incapable of being implemented”.

“Every student in Australia will be treated exactly the same way regardless of what jurisdiction they’re in,” he said.

Mr Abbott said the mid-year economic and fiscal outlook due in December would make it clear how the government would account for the $1.2 billion.

“We have identified appropriate savings over and above the savings that we identified prior to the election,” Mr Abbott said.

The government will review the schools funding system in 2015, in line with legislative requirements.

It has also not committed to the full six years of funding proposed by Labor – a move criticised by the Australian Education Union.

Its deputy president Correna Haythorpe says the Government is effectively only committing to a third of the funding promised to the states that signed up to Gonski.

She says most of the funding would have flowed in the last two years of the six year agreements.

“Today’s statement has done little to provide certainty for Australian schools,” she said.

She said kids in the NT, Western Australia and Queensland had been short-changed as these states would get federal money without having to co-contribute.

Some of the states which had signed on to the original Labor deal remained guarded in their enthusiasm for the latest version.

“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”.

Mr Shorten says Government has put education sector on a ‘rollercoaster’

The Opposition Leader has described the policy reversal as “the latest saga in the coalition’s election promise-breaking antics in education”.

In parliament later in the day, Mr Shorten rounded off the series of questions by asking “when will the Prime Minister stop lying?” – a phrase he was forced to withdraw.

The questions gave the Prime Minister the opportunity to criticise Labor over its failure to secure a national agreement on schools funding while in government.

“I want to make it absolutely crystal clear that this Government is cleaning up Labor’s mess,” Mr Abbott said.

Mr Shorten then moved the new parliament’s first motion of censure in the Prime Minister, “for breaking his promise to parents and children across Australia that no school will be worse off under his Government”.

But the Government used its numbers to instead censure the Opposition Leader for cutting funding to the hold-out states and “failing to achieve a national, fair and needs-based school funding mode”.

The $15.2 billion Better Schools Plan was based on recommendations made by a review panel which was chaired by businessman David Gonski.

Sixty-five per cent of the additional money was slated to come from federal coffers with the rest contributed by states and territories.

The government has also said it will honour $55 million for Catholic education commissions and $110 million for the Association of Independent Schools, something welcomed by the National Catholic Education Commission.