Tony Abbott has downplayed concerns his government may introduce GP co-payments, saying he won't change his spots when it comes to being the best friend of Medicare.

Health Minister Peter Dutton has been accused of softening up voters for the introduction of co-payments by saying Medicare is unsustainable and that the better-off might need to pay more.

Co-payments of up to $6 to visit the doctor have been flagged as one way to tackle spiralling health spending, as the commission of audit investigates ways to rein in the budget deficit.

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The prime minister acknowledged the country's finances were under pressure and it was "very important that we do what we can to fix the budget as quickly as we can".

However, Mr Abbott said any savings measures had to be consistent with the coalition's pre-election commitments.

"Don't forget, I said we were going to be a no-surprises, no excuses government," he told reporters in Sydney.

Mr Abbott pointed to his remark when he was health minister that the then Howard government was the best friend Medicare ever had.

"This leopard doesn't change his spots," he said.

"I want this government to be likewise the best friend that Medicare has ever had."

Despite the prime minister previously stating "nothing is being considered, nothing has been proposed, nothing is planned" on GP co-payments, Mr Dutton said a national conversation was needed on how to pay for rising health costs.

Mr Dutton said many Australians already made a co-contribution on prescription medicines and private health cover, while others were already paying to see a GP.

He wants a discussion about whether people on "reasonable incomes" should expect to pay nothing when they go to a doctor.

Labor leader Bill Shorten said Labor would fight any moves to dismantle Medicare, and accused the government of having a secret plan to introduce a new GP tax.

"(Mr Abbott) promised before the election he would protect Medicare, but now he is trying to destroy our universal healthcare system," Mr Shorten said.

Health groups have condemned the idea, with the Australian Medical Association saying it would deter people from seeing their GP.

The Consumers Health Forum said many Australians already struggled to meet their rising health costs, and labelled co-payments a tax on the sick.

The Australian Healthcare and Hospitals Association said co-payments would provide limited financial savings, with the burden instead being shifted to emergency departments.

Greens health spokesman Richard Di Natale said it would take Australia towards a US-style health system, where many can't afford basic health care.