Tony Abbott has declared the GP co-payment as "dead, buried and cremated" after it was finally dumped on Tuesday.

The Prime Minister's office emphatically rejected a claim, first reported by Fairfax Media, that Mr Abbott had chided his former health minister Peter Dutton in cabinet on Monday over the bungled co-payment "barnacle"..

The government has now abandoned the patient charge, or "value signal in health" as it was described at one point, with Mr Abbott invoking his post-WorkChoices formula to brand the 2014 budget's $7 co-payment as "dead, buried and cremated".

Its demise followed several iterations which included reducing it to $5 in a failed attempt to soften its impact, and even briefing media that it had been dropped altogether in December before resuscitating it the next day.

An unusually chastened Mr Abbott moved to assume the blame for the politically disastrous policy in question time, declaring he had listened and learnt and that he should have known that wider consultation was needed to undertake such significant reform.

He also acknowledged that it should always have been a matter of working with doctors, rather than being seen to work against them.

A source had told Fairfax Media that in cabinet, Mr Abbott had characterised the sales job as "mishandled until now", which was interpreted as a swipe at Mr Dutton, who is now Immigration Minister.

The new Health Minister Sussan Ley had been charged with consulting with doctors but, with no sign of their support, the government decided it had taken enough water over the plan.

In its place, Ms Ley has been asked to work with GPs and the medical profession to find other savings in the system.

That is unlikely to secure the longer-term structural savings needed to rein in Medicare, which is projected to cost $34 billion within a decade, up from its current $20 billion cost.

Doctors' groups welcomed the move and have now called for an end to the freeze on the indexation of rebates as well.

Australian Medical Association president Brian Owler said the freeze could lead to doctors shortening their consultations, or charging more patients the full cost of their visit upfront. Because the freeze also applies to rebates for specialists, Associate Professor Owler said it would also increase out-of-pocket costs for surgical procedures, including for people who have private health insurance.

But Associate Professor Owler praised Ms Ley's "constructive and consultative approach" and said he was hopeful of persuading her to lift the freeze.

"We've already had very productive discussions with the Minister, around ways that we might try and curtail the freeze to indexation. I think that issue is not at an end," he said.

Royal Australian College of General Practitioners vice-president Morton Rawlin said the government had acted in the best interests of patients by dumping the co-payment, but he called for an end to the freeze on rebate indexation.

"Continuing the freeze will force GPs to pass on increasing out-of-pocket costs to patients; threaten the provision of quality clinical services; place recurring pressure on the business viability of practices; and increase health system costs downstream," Dr Rawlin said.

Terry Barnes, a former health advisor to Mr Abbott whose submission to the Commission of Audit placed the co-payment on the political agenda, said taking the co-payment off the table was "sensible and overdue".

"It clearly was a barrier to making progress towards comprehensive structural reform of Medicare," he said.

But while he praised Ms Ley's consultative approach, he said the AMA "should not have a right of veto over the direction of health policy in Australia".

Mr Abbott said he had learnt from not bringing stake-holders into the policy-making process. "As a former health minister I suppose I should have been more conscious of this," he said.

"I accept, I accept that it's taken us some time to come to this position. I do accept that it's taken us some time to come to this position."