Nine out of every 10 teachers who voted in a ballot over pay in England and Wales were in favour of striking, a union says.
But the NASUWT union also reported a 42% turnout - below the threshold needed for lawful strike action.
Its general secretary, Dr Patrick Roach, said the union remained in formal disputes over pay.
The government said it would continue talks to avoid any "damaging" industrial action.
Dr Roach said NASUWT members were "sending a strong message to the government".
"The readiness of our members to support industrial action demonstrates the anger of the profession and the need for governments in England and Wales to engage in meaningful negotiations to address the deep concerns of our members," he added.
