Prime Minister Malcolm Turnbull says he's not wedded to his government funding the full Gonski education plan.
Rather than harking back to Labor's "barely credible" $80 billion funding promises, the focus should be on achieving the best outcomes for students with the limited resources available, he says.
Mr Turnbull said Australia had a serious structural budget problem, with Treasury revising down revenue forecasts every six months since 2011.
"We have to be clear-eyed about our choices - how do we get improvements to our infrastructure and central public services when there are more demands on government but less revenue available to pay for it," he told reporters following Friday's meeting of the Council of Australian Government.
Under the Gonski plan - from a report by consultant David Gonski - two-thirds of extra schools revenue was to have come from the federal government and a third from the states. The federal government would take most of the responsibility for supporting disadvantaged schools.
It's estimated that would cost an extra $4.5 billion in 2018 and 2019.
That's strongly supported by Labor. Teachers and their unions have recently stepped up a campaign calling for the government to stick to the Gonski funding plan.
The COAG communique said the commonwealth contribution to schools education was agreed through to the end of 2017.
Discussions on new funding arrangements should be concluded by early 2017.
"Much as I admire David Gonski, we are not wedded to that particular - the 'full Gonski' - whatever that means," Mr Turnbull said.
The prime minister said the COAG meeting had made clear that states would not support levying their own income tax and the commonwealth would not be lifting tax rates.
"Then we have to work within our existing fiscal envelope," he said.
However, NSW Premier Mike Baird said the federal government had "left open the option" of supporting the Gonski schools agreement beyond January 2018.
"NSW has committed to it, remains committed to it, and continues to seek and will continue to argue for its funding on an ongoing basis," he said.
West Australian Premier Colin Barnett said he never believed the $80 billion Gonski funding promised by former Labor prime minister Julia Gillard was realistic or could be properly funded.
"Mike Baird and others have made it clear, funding health is our biggest challenge right across Australia," he said.
