Malcolm Turnbull says the states must fund any increase in spending on schools and hospitals and not expect Canberra to be an ATM.
The ultimatum came as the prime minister said his tax plan, which would ensure any change does not result in overall federal taxes rising, could be released before the May budget.
Mr Turnbull is facing a backlash from within the coalition over a possible rise in the rate of the GST from 10 per cent to 15 per cent.
At the same time, Labor and the states have urged the government to boost spending on schools and hospitals.
Mr Turnbull said the states needed to take a careful look at their own taxes, such as stamp duties, and his government would not raise taxes just to spend more.
"They (the states) have got to be prepared ... to go to their citizens and say ... `we need to raise more money to spend on our schools and our hospitals and we are going to increase this state tax or that state tax'," he told 5AA radio in Adelaide on Friday.
The federal government would no longer be an ATM for the states.
South Australian Premier Jay Weatherill said he would not accept a rise in the GST unless there was a "revenue fix" that covered the $80 billion in health and education cuts.
Mr Weatherill and NSW Premier Mike Baird have proposed the GST rate rise to 15 per cent with households compensated and the net proceeds going towards the fiscal gap in health, estimated to be $35 billion a year by 2030.
"Health funding is now shaping as the key federal election issue," Mr Weatherill said on Friday.
Mr Turnbull said any change in the tax mix would ensure the less well-off were properly compensated and that it had a productivity benefit.
He was "thrilled" that tax was being debated within the coalition and more broadly.
"When we come to a decision, which we will do shortly ... people will be able to say, even if they don't agree with us, that we thought about these issues carefully," Mr Turnbull said.
Nationals MP Michelle Landry says small businesses in her seat of Capricornia have contacted her with concerns about a GST rise.
"I'd prefer to see the GST stay as it is and maybe look at some other avenues with the tax reform," she told ABC radio.
Liberal MP Dan Tehan said keeping the tax system as it was would lead to higher taxes for average income earners and long-term economic decline.
Shadow Treasurer Chris Bowen said the Liberal party was "at war with itself" on tax.
