The federal health minister, Peter Dutton, has signalled dramatic changes to Medicare to address “staggering” increases in health spending, confirming the Abbott government would consider a new fee for visits to the doctor.

Laying the groundwork for politically sensitive reforms, Dutton said he wanted to “start a national conversation about modernising and strengthening Medicare”. He said the health system was “riddled with inefficiency and waste” and warned that doing nothing to address the long-term budget burden was not an option.

In a speech in Brisbane on Wednesday, the minister flagged a greater role for the private sector and private insurers in primary care as the government wanted to “grow the opportunity for those Australians who can afford to do so to contribute to their own healthcare costs”.

But Labor seized on his comments of evidence that the government planned “to destroy universal healthcare in Australia” by making people pay more to access services.

The shadow health minister, Catherine King, said Dutton’s claims about rising health costs were “hysterical” as Australia spent 9.1% of its gross domestic product on health compared with 17% by the United States.

Dutton followed up his speech with an interview on the ABC’s 7.30 program in which he said the country should debate how governments and consumers paid for health services. He said the discussion should include payment models for people who had “a means to contribute to their own healthcare”.

The minister told the program: “I want to make sure that, for argument’s sake, we have a discussion about you or me on reasonable incomes, whether we should expect to pay nothing when we go to see the doctor, when we go to have a blood test – should we expect to pay nothing as a co-contribution and other taxpayers to pick up that bill?”

Asked about the idea of a new $6 co-payment for bulk-billed GP visits, which was raised in a submission to the National Commission of Audit, Dutton said suggestions had been made in favour and against the proposal but it was “one aspect that the government will need to consider”.

“Well, my own view is that people at the moment pay a co-contribution through when they buy their medicines, regardless of their income,” Dutton said.

“People pay as little as $6 for a $17,000 prescription, a single prescription. People pay a co-payment at the moment for their private health insurance. Eleven million Australians have private health insurance.

“Many Australians already pay a co-payment when they go to see a doctor. Now, the issue is how you guarantee access, particularly for those who are without means, and how you don’t deter people from going to see a doctor if there is some sort of a payment mechanism in place.”

In the leadup to the 8 February Griffith byelection, Tony Abbott dismissed a Labor “scare campaign” over a new fee for bulk-billed GP visits.

The prime minister refused to rule it out, but played down the prospect. “Nothing is being considered; nothing has been proposed; nothing is planned,” Abbott said on 1 February.

On Wednesday night the opposition sounded the alarm over the prospect of a “GP tax”, saying Australians should get the healthcare they needed rather than what they could afford.

“The Liberal party has never believed in Medicare and they have never believed in a universal healthcare system,” King said.

“Australians who can afford to pay more already do so through a greater contribution to the Medicare levy. What Mr Dutton is really talking about is dismantling our fair and sustainable system in favour of a private health system like that which exists in the United States.”

Earlier, Dutton said in his speech that there were “many shrill voices” decrying the government-ordered commission of audit despite the need to address federal debt and deficit.

The focus of the minister’s address to the Committee for Economic Development of Australia was the rising cost to the budget of health services, with the prospect of even bigger increases as the population aged and the country confronted obesity, diabetes and dementia challenges.

Dutton said total spending on healthcare in Australia had increased by 122% in the 10 years to 2011-12, when it totalled $140bn. This equated to about $6,200 a person a year on average.

The commonwealth component of health spending was forecast to rise from $62bn now to $75bn by 2016-17.

Dutton described Australia’s “1980s model” health system as “tracking on an unsustainable path with no prospect of meeting the needs of the health of our nation in the 21st century”.

“There’s been talk about simply increasing the Medicare levy to solve the sustainability issue. Let me just say here [that] if we were to increase the Medicare levy to cover the entire cost of the commonwealth’s health budget, it would have to increase to 9.5%. That’s $7,220 per year on an average salary of $77,000.

“Either way, individuals end up paying for their healthcare – whether it is directly or indirectly through pay as you go or through higher taxes otherwise. To reap the benefits, there’s always a cost, and I think most Australian taxpayers understand this.”

Dutton said governments met about 70% of total spending on healthcare in Australia while individuals directly contributed about 17% through out-of-pocket payments.

He said there would “always be value in leveraging people into supporting their own health needs in the private sector”, arguing that picking up nearly 100% of the cost made “no sense” for the taxpayer when the patient was prepared to contribute to their own costs.

The minister said governments contributed about 35 cents in the dollar for private hospital services – including through the Medicare Benefits Schedule and the private health insurance rebate – but 92 cents in the dollar for those treated in the public system.

“Therefore one important job of the Abbott government is to grow the opportunity for those Australians who can afford to do so to contribute to their own healthcare costs,” he said.

Dutton voiced support for allowing greater involvement of private health insurers in primary care, asking: “Why should we see the private sector involving itself in public services as a bad thing?”

He also called for “improved public sector efficiency” in the health sector.