Giving the states full responsibility for funding public schools, as proposed by Prime Minister Malcolm Turnbull, would be the biggest mistake in the history of Australian education policy, according to NSW Education Minister Adrian Piccoli.

A war of words has erupted between the NSW and federal education ministers just months before the federal election, with Mr Piccoli accusing his Coalition colleague, Simon Birmingham, of making "incomprehensible" claims about the relationship between school funding and academic results.

Senator Birmingham shot back, accusing Mr Piccoli of perpetuating "class warfare" and "defying mathematical logic" by calling for extra money from Canberra for NSW schools.

Mr Turnbull last week said the federal government could withdraw from funding public schools, while continuing to fund non-government schools, if it gave state governments a share of income tax revenue.