The Post Primary Teachers Association has told members the dispute over their collective agreement could be difficult and long.
The PPTA began its annual meeting on Tuesday by warning members that their industrial action over stalled pay talks could even continue into next year.
President Kate Gainsford later said the union had no indication that that might happen, but it was possible.
Ms Gainsford told delegates the Government may choose to lock teachers out if they refuse to teach on some days - if that happens, she says, the teachers will strike.
Education Minister Anne Tolley says, however, that she has heard no talk of lockouts. Ms Tolley told the meeting that she values teachers and that the Government wants to negotiate a settlement.
She says the union needs to return to bargaining.
PPTA members told Radio New Zealand they are fighting for public education and are determined to stand firm.