The NAHT has become the latest union to vote against the government's pay offer to teachers - raising the possibility of more strikes.
School leaders have overwhelming rejected the government's pay offer to teachers, raising the prospect of further strike disruption.
The National Association of Head Teachers (NAHT) is the latest education union to vote down the deal, following in the footsteps of the ASCL (Association of School and College Leaders) and NEU.
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Over 90% of members knocked back the "inadequate and unaffordable" offer, saying they did not have the headroom in their budget to be able to pay for it for the next academic year.
Paul Whiteman, NAHT general secretary, said: "Our members do not recognise the government's calculations on the affordability of the offer, with the vast majority of head teachers and school business leaders saying they could not pay the rise from their existing budgets.
"This is a very clear stumbling block and one the government must listen to and solve if we hope to bring this dispute to an end."
The NAHT said it will now consult on next steps - including a formal ballot on industrial action.
Nearly four in five (78%) NAHT members said they would be prepared to vote for this, up to and including striking, if the offer was rejected.
Mr Whiteman urged the government to "come back to the table and solve this dispute".
"To do otherwise would be to stick two fingers up to a dedicated profession whilst at the same time turning their backs on children."
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Pupils in England already face missing five days of school next term after the National Education Union (NEU) approved more walkouts.
Delegates at the NEU's annual conference on Tuesday voted in support of a three-day strike in late June/early July.
The teaching union had previously announced two further strike days on 27 April and 2 May after 98% of its members voted to turn down the government's pay offer.
Ministers offered teachers a £1,000 one-off payment for the current school year (2022/23) and an average 4.5% pay rise for staff next year (2023/24).
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But questions have been raised over funding with 4% expected to come out of existing school budgets and the rest provided for by government.
The NEU said between 42% and 58% of schools would have to make cuts to afford it.
And the ASCL called it "inadequate in every respect", with 87% of members, voting to turn down the deal on Tuesday.
The ASCL's executive committee will reconvene after the Easter break to consider its next steps.
A Department of Education (DfE) spokeswoman said: "After costing children almost a week of time in the classroom and with exams fast approaching, it is extremely disappointing that the NEU are re-balloting for more strike action up until Christmas this year."