The NASUWT union says it will consider going on strike in the autumn term.
More teacher strikes could hit schools in England, after a second education union voted to walk out over pay.
The NASUWT union said 88.5% of around 122,000 balloted members voted for strike action, with a 51.9% turnout.
A larger union, the National Education Union (NEU), has already held seven national strike days since February and is re-balloting members for more action in the autumn.
NASUWT said it plans to begin action short of a strike in September.
It has not given further detail about what that action could involve, but action short of a strike taken by teachers in other unions this year has included refusing to provide lunchtime supervision or to attend meetings held outside working hours.
The union said it would consider going on strike in the autumn term, and that it would co-ordinate action with any other education unions that vote to walk out.
NASUWT teachers in 56 sixth form colleges have already backed strike action so would also be expected to join any action.
Dr Patrick Roach, NASUWT’s general secretary, said the vote was the largest mandate the union had secured for industrial action in more than a decade.
“Today our members have sent a strong message to the government and to employers that teachers demand a better deal on pay and to address excessive workload and working hours,” he added.
The four teaching unions involved in the dispute with the government want an above-inflation pay increase, plus extra money to ensure any pay rises do not come from schools’ existing budgets.
Most state school teachers in England had a 5% pay rise for the year 2022-23.
After intensive talks, the government offered an additional one-off payment of £1,000. It also increased the offer for most teachers next year to 4.3%, with starting salaries reaching £30,000.
The Department for Education (DfE) described it as a “fair and reasonable offer” and said schools would receive an extra £2.3bn over the next two years.
But all four unions involved in the dispute rejected the offer.
The DfE has been contacted for comment about NASUWT’s announcement.