Malcolm Turnbull will go it alone on tax reform if he can't get a deal with the states early next year.
The prime minister's first Council of Australian Governments meeting, held in Sydney on Friday, ended without an agreement on changing the tax system.
But Mr Turnbull expressed hope a deal could be struck at the next meeting in March, held in the leadup to his first federal budget since ousting Tony Abbott in September.
"I believe there is enough goodwill to be able to reach agreement on that, but if there is not then we won't and then we will have to make decisions within our own jurisdictions," Mr Turnbull told reporters after the meeting.
He acknowledged there was no consensus on a way forward, but making changes to the GST, Medicare levy and income tax remained on the table.
The premiers skewed the talks towards how to fund the health system, which is under pressure as the Australian population ages.
Mr Turnbull said the federal government would not be revisiting cuts slated in the 2014 budget, which totalled $80 billion for schools and hospitals.
"Rather than going into history let's look at the challenge going forward," he said.
NSW Premier Mike Baird said the leaders had agreed the top issue was how to fund health.
If an agreement could not be struck in March the premiers would settle for an interim deal starting in July 2017.
"We have committed ... to investigating all tax options as a way of addressing this challenge," Mr Baird said.
"We've gone through them before - the GST, the Medicare levy, income tax sharing, together with state tax options and we're committed to doing this together."
South Australian Premier Jay Weatherill said extra funding was crucial.
"Without this solution we will have to (consider) ... closing actual hospitals - that's the size of the health care funding crisis that needs to be addressed in these discussions," he said.
The premiers agreed on new laws allowing convicted terrorists who complete their jail terms to remain imprisoned if they still pose a risk, and preventative detention before charges are laid.
An ice action strategy and plan to ensure domestic violence orders apply nationally were also agreed.
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