Prime Minister Julia Gillard has dismissed claims from Premier Colin Barnett that the Gonski review of school funding is a federal attempt to take over state-run schools.
Mr Barnett has accused the federal government of wanting to pool state education funds and then administer the schools.
"Sorry, ain't gonna happen," the Liberal premier said on Tuesday.
But Ms Gillard says the premier has his facts wrong.
"I am concerned Premier Barnett would somehow take a message from this major review on school funding that it is about who controls schools," she told reporters in north Adelaide on Wednesday.
"It's not about who controls schools - states will continue to manage and control public schools.
"This is about governments working together to get (school funding) right for the future."
The prime minister said Mr Barnett would continue to lead the WA public education system.
South Australian Premier Jay Weatherill told reporters his Labor government supported the principles underpinning the Gonski review.
"I don't think it threatens states' autonomy to run education systems," he said at a joint press conference with Ms Gillard.
"If you care about public education then it simply does not make sense to have state governments funding public education and the commonwealth government funding private education.
"One system will, over time, become a less well-supported system."
Mr Weatherill said both levels of government needed to support all children, whatever school they attended.
The federal government this week released the findings of an independent school funding review by businessman David Gonski and Labor's initial response.
The review recommended funding per student be based on a new national standard that reflects the actual resources used by schools which consistently achieve high results.
It called for a $5 billion funding boost and said Australian governments must spend more money on schools with high numbers of disadvantaged students.
