State and territory leaders have flatly rejected Malcolm Turnbull's radical plan to have them assume a portion of income taxing powers, unceremoniously consigning the idea to the political dustbin.

And they notched up another win also on short-term health and hospital funding signing a heads of agreement document with the Commonwealth for an extra $2.9 billion from July 2017, to 30 June 2020, along with a lift in the 6 per cent cap in the growth of Commonwealth funding to 6.5 per cent.

That led NSW Premier Mike Baird to declare his state could now manage its hospital expenditures to the end of the decade, even if beyond that, the combination of health inflation and demographic change would see the situation worsen again.

However, Victoria's Labor Premier Daniel Andrews was less positive, stating the restoration of "hundreds of millions of dollars" did not not replace the "billions of dollars" stripped from the state in the 2014 budget.

Mr Turnbull called "it substantial funding at a substantial growth rate".

But in an embarrassing repudiation of what just two days ago Mr Turnbull had championed as "the most fundamental reform to the federation in generations" and "the only way that we can genuinely reform our federation", first ministers emerged from Friday's the Council of Australian Governments firmly convinced that transferring the power to set a portion of income tax to the states to fund hospitals and schools would generate multiple new problems.

"There isn't anything like a consensus," Mr Turnbull acknowledged, declaring his preferred model was finished. "It's withdrawn, it's not acceptable," he said.

In a clear public defeat, the ambitious plan had come and gone in the space of just three working days after being revealed by the Prime Minister in a doorstop press conference on Tuesday, albeit without any supporting documentation.

It had also been spruiked by Treasurer Scott Morrison.

But the scale of the change and the method of its announcement had immediately put premiers' noses out of joint.

Speaking immediately after Mr Turnbull's frank admission of defeat, flanked by the other leaders, the County Liberal Party Chief Minister of the Northern Territory, Adam Giles, said: "in regards to the income tax discussion, I think we can all agree that it would have been best if that discussion came out in a different format, in a different way, and it has created some challenges to date".

In its place, leaders resolved to examine a counter-proposal closer in substance to one suggested months ago by South Australia's Labor premier Jay Weatherill.

It would see states gain direct access to a fixed percentage of the growing income tax pool, in replacement for tied or special-purpose grants from the Commonwealth. The advantage to the states would come through greater autonomy to decide their own spending, but the total proportion of revenue would remain fixed.

"The states will not be levying an income tax and the Commonwealth will not be increasing income tax," Mr Turnbull noted, "so our federation reform process has to be focused on how to work within the current fiscal envelope to achieve the best long-term solution, most efficiently, to funding our schools and hospitals."

Mr Turnbull said the new approach would provide the states with "greater financial autonomy to do their job of managing their affairs in the interests of the citizens they serve".

However, Mr Turnbull was able to claim some wins from the talks after extracting a commitment from states to embark on genuine internal reform of their revenue raising and transparency measures.

This would include beginning the process of internal reform and the shift from inefficient taxes such as stamp duties, towards more efficient and equitable ones such as land taxes.

"COAG further agreed to continue pursuing initiatives that will enhance transparency by providing Australian citizens with a greater level of real time data on how government money is spent and on the outcomes and performance of government initiatives.

The extra $2.9 billion for hospitals represents a minor retreat from the Coalition's plan to cut $57 billion from health over a decade.

In exchange, the states agreed to reduce demand for hospitals through "avoidable" admissions, and supporting its chronic health package.

The federal government also agreed to slightly increase the Coalition's cap on the growth rate of health funding from 6 to 6.5 per cent.

Mr Turnbull, when asked whether he was confident the current fiscal envelope could provide decent schools and education, said: "The agreement today delivers substantial funding at a substantial growth rate."

Labor premiers criticised the health agreement shortly after signing it, saying it did little to reverse the damage the cuts would wreak on hospitals and patients from next year, when funding would slow dramatically.

Victorian Premier Daniel Andrews said that while the agreement was positive "there's no getting away from or getting around or politely explaining away the fact that many billions of dollars will not be flowing to hospitals in my state and hospitals right across the nation as a result of decisions made in the 2014 budget".

The Australian Medical Association's president Dr Brian Owler said the public and hospital workers were "right to be disappointed" in the agreement. He said the additional funding would help relieve some pressure from public hospitals "but the pressure will remain and build once this short-term fix expires."

With Jane Lee and Michael Koziol

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