"Should a bilateral agreement not be in place by this date,the Commonwealth will be unable to make the first 2019 payment to the relevant state or territory,including with respect to non-government schools,"Mr Tehan said in a letter sent to NSW Education Minister Rob Stokes on Wednesday.
"In these circumstances,I would seek your assurance that the[NSW] government would make up any shortfall experienced by the non-government sector to ensure that schools do not face undue financial stress."
The letter signals the Coalition's urgency to resolve the uncertainty around school funding after it surprised the states last week by announcinga further injection of $4.6 billion into independent and Catholic schools.
Victorian Education Minister James Merlino was furious,saying Mr Tehan was holding a gun to the heads of states and territories by inventing deadlines.
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But Mr Stokes just reiterated his commitment to needs-based,sector-blind school funding."Fair funding for school children is an important issue and I look forward to continuing to work with the federal government to find a solution,"he said.
Mr Stokes is due to have a meeting - likely to be by phone - with Mr Tehan on Friday.