Education Minister Anne Tolley says she expects school boards that oppose the national standards in reading, writing and maths to change their minds.
A group of several hundred schools has refused to include targets based on the national standards in their charter documents, as required by the Government.
Mrs Tolley told Radio New Zealand's Insight programme that sacking the schools' boards would be a last resort, and she hopes it won't be necessary.
"I've found by and large," she says, "that boards of trustees, once they've understood properly what the standards can do and the information that it can give them, and then the support that's coming in behind that, have had a rethink - certainly the ones that I've been talking with.
"And I think that will happen over a period of time."
A spokesperson for the schools, the principal of Island Bay School in Wellington, Perry Rush, says they will not back down. The 350 schools in the group hope others will join them.
The Ministry of Education says it has considered the charters of 1300 schools, and 87% of them have included targets based on the standards.
Altogether, about 2300 schools are required to set targets.