Older Australians on the pension, set to fork out more for private health insurance due to government budget measures, will face ”unfair” cost pressures, according to an independent MP.

Labor announced the scrapping of the private health insurance rebate for Australians over 65s in May as a measure to address intergenerational inequity and to help fund aged care.

The rebate people receive depends on your income, though some older people currently recoup eight per cent more than others on the same earnings. Ending that would save $3 billion over four years, according to the most recent federal budget.

On Monday, modelling from the Parliamentary Budget Office showed about $1.6 billion of the projected savings will come from pensioners by the end of the decade.

Independent MP Monique Ryan labelled the rebate cut a cash grab that unfairly targets pensioners who should be carved out from the legislation.

“Punching down on old people in what it claims to be a way of finding cash for aged care is not the way to go about private health insurance reform,” Ms Ryan said on Monday.

“Now that’s going to take away half of the potential financial benefit of it, which I would say brings into question the work of this legislation at all. I would really like to see it shelved.”

Removing the Howard-era rebate is a lazy tax on pensioners, according to coalition health spokeswoman Anne Ruston.

“The government have got no idea about the details that sit behind this,” Senator Ruston told reporters.

“They still haven’t modelled the cost on our public hospital system, and we know that states and territories are already out there yelling and screaming about the impact on them.”

Australian Medical Association chief Danielle McMullen said the changes would likely shift costs to the public sector by removing the incentive for older Australians to hold on to private health insurance.

“This is at a time when the private health sector is facing significant pressures and our public hospitals are under considerable strain,” Ms McMullen said recently.

Health Minister Mark Butler’s office has been contacted for comment.