The Greens plan to ditch the private health insurance rebate and reinvest billions of dollars of savings into the public health system, leader Richard Di Natale has announced.

The rebate of up to 30% of the cost private health insurance is a $5bn expense in the federal budget.

The Greens have released parliamentary budget office costings which show that phasing it out over the next two years could save $9.7bn by the 2018-19 financial year.

“It’s never easy to talk about withdrawing subsidies in an election year. But the Greens have the courage to call the private health insurance rebate what it is – unfair, inflationary and inefficient,” Di Natale said.

“The private health insurance rebate is a public policy disaster that has completely failed to achieve its stated objective of easing pressure on public hospitals.

“If the $5bn-a-year subsidy [were] reinvested back into the public health system it would take the pressure off hospital waiting lists, reduce waiting times in the emergency department and help fund public dental care,” he said.

The Greens policy said people with private health insurance continued to use services at public hospitals because they were of high quality and specialised in complex and urgent care that many private hospitals could not, or would not, perform.

It cited a University of Melbourne research paper which found that scrapping the rebate would save two and a half times as much money as the increased public health costs of people using the public system more as a result.

The Australian Council of Social Services (Acoss) has called for the private health insurance rebate to be scrapped.

Acoss chief executive, Cassandra Goldie, has said the rebate “disproportionately benefits people on higher incomes who can afford private cover in the first place, and has been a significant factor in driving up costs without any evident gain in achieving its initial policy intent”.

Di Natale announced the Greens would restore the funding model where the commonwealth and the states share the rising costs in delivering hospital services evenly.

The party would also enshrine the funding formula into law, to give states certainty about health funding and require parliament’s approval if a future government attempted to reduce the share of hospital funding from the commonwealth.

Di Natale also lashed the government’s plan for states to pay for shortfalls in health spending after cuts in the 2014 budget, labelling it “the latest thought bubble from a dithering government without the vision or courage to take on real reform”.

“The Abbott/Turnbull government has taken Australia’s hospitals to the edge of a funding cliff that will decimate the health system and its only proposal for dealing with this issue is to dump the problem entirely on the states and territories in a desperate act of political cowardice,” he said.

“Private health insurance is a legitimate choice for many people, but the Greens want to build a world-class public health system, so that private health insurance remains a choice rather than a necessity.”