Australian universities will be spared about $2.3bn in cuts after Labor announced it would reverse its position and combine with the Greens to block savings it proposed when in government.

The prospect of a $2.3bn hole in the federal budget, a day after the government earmarked another $1.2bn for school funding, brings to $3.5bn the savings the Abbott government must find as a result of education policy developments this week.

The federal government on Tuesday defended its decision to offer school funding to the states with “no strings” attached, dismissing concerns states would no longer be formally obliged to increase their spending in return for the extra commonwealth support.

Education dominated parliamentary question time on Tuesday, with the opposition leader, Bill Shorten, labelling the “panicked school deal” a con that did not require states to increase their contributions by 3% annually.

The prime minister, Tony Abbott, said the only con was the former government’s decision to remove $1.2bn in budgeted school funding before the election as a result of a failure to reach agreements with the conservative-led states of Western Australia, Queensland and the Northern Territory. Abbott said he was responsible only for the federal government’s actions, not those of the states, which owned and operated public schools.

In April the Labor government under Julia Gillard pursued the university efficiency dividend and removal of incentives for early repayment of Hecs-Help as a way to help fund the David Gonski-inspired school funding reforms. At the time it was accused of “robbing Peter to pay Paul”.

But Labor did not legislate the savings before the election, leaving it to the incoming Coalition government to push the measures through parliament. Labor has been capitalising in the past week on shifts in the government’s schools policy, accusing it of undermining the Gonski reforms.

Labor said on Tuesday it could no longer support the higher education savings when the Coalition had “abandoned the six-year plan [the cuts] were designed to fund”.

Labor’s higher education spokesman, Kim Carr, said the Gillard government had proposed the savings for a specific purpose – to target imbalances and inequalities in the school funding system.

“In return for increased funding our six-year plan stopped signatory states from cutting funding to schools and ensured that they would not only maintain but increase the amount of money flowing to students,” Carr said in a statement.

He said the Abbott government had abandoned “a meaningful six-year reform program” and handed the states a blank cheque with no guarantees students would benefit.

Before the election, the Coalition said it was on a “unity ticket” with Labor on school funding, but promised to match only the $2.8bn allocated in the first four years of the six-year plan. Most extra school funding was earmarked for the final two years beyond the four-year budget cycle.

The education minister, Christopher Pyne, indicated last week he would keep the Gonski-inspired reforms only for the first year of implementation (2014) and would devise a new system to apply the following year. The education minister then announced $230m for one year of funding for the hold-out jurisdictions of Western Australia, Queensland and the Northern Territory, prompting an outcry from states that had already signed up amid fears they would lose money after 2014.

Abbott and Pyne sought to defuse the controversy on Monday, following accusations from state education ministers, notably including the NSW Coalition education minister Adrian Piccoli, that the government had broken its election promises. They vowed to fully reinstate the $1.2bn earmarked for the three hold-out jurisdictions and dumped plans to rewrite the funding model after 2014, saying each state would get exactly the same four-year deal envisaged under Labor.

But the government would proceed with the Coalition’s long-promised removal of “command and control” elements of the legislation, reducing the regulation of state education spending.

In question time on Tuesday, Pyne said officials were still finalising the details of the in-principle agreements with the three jurisdictions to benefit from the restoration of the $1.2bn, but the government was treating the states as “adult” administrators.

The Greens had previously called on Labor to side with them in the Senate to block the university savings on the basis of the Gonski reforms not being fully implemented.

Labor and the Greens have the numbers in the Senate to block legislation until the new upper house sits in July.

The Greens’ spokeswoman on higher education, Lee Rhiannon, said the decision would restore funding to universities and save disadvantaged students from incurring more debt through changes to a scholarship program.

Rhiannon acknowledged many universities had already been planning ways of dealing with the expected efficiency dividend next year and urged them to reinstate any staff members who lost their jobs as a result.

“It’s certainly not too late but the pressure will now be on universities and I’m sure the staff, students and their respective unions,” she said.

Pyne presented a bill to the lower house last month to implement some of the university savings devised by Labor. They included an efficiency dividend of 2% to apply to Commonwealth contributions under the Commonwealth Grant Scheme in 2014, and 1.25% the following year, saving $903m over four years.

A further $277m would be saved by the removal of the 10% discount for up-front payment of Hecs-Help fees and the 5% bonus for voluntary Help repayments of $500 or more.

Labor will vote against Pyne’s bill and will also oppose a measure in another bill introduced by the social services minister, Kevin Andrews. The second bill deals with several measures including gambling but includes one of Labor’s other proposed savings: the conversion of student start-up scholarships to loans.

Introducing his bill during the last fortnight’s parliamentary sitting, Pyne said the government had no choice but to proceed with the savings given the budget position it inherited. He sought to portray the savings as “Labor’s cuts” which showed “just how damaging to the university sector the previous government was”.

The government announced last month it would abandon one of Labor’s education savings – the capping of tax deductions for self-education expenses.

Both sides of politics have been subject to intense lobbying by the higher education sector.

The chief executive of Universities Australia, Belinda Robinson, said Labor’s announcement was pleasing but there was “a way to go until the fate of these cuts” was finally determined.