The president of the Principals' Federation says data collected from national standards should not be made public.
On Friday, the Government released an overall snapshot of national standards achievements and on 28 September will make available official school-by-school data online.
Principals' Federation president Paul Drummond says the information should stay within schools and be reported to parents, the Education Review Office and the Education Ministry as they wish.
He says the national standards, which measure reading, writing and maths, are not wide enough, and should cover other subjects as well.
Education Minister Hekia Parata says the point of national standards is to raise achievement, and the data is essential.
"The information in the first instance is for learners, their parents and the school to do something about raising (achievement), and for us as a Government, we want to be able to look across the entire system and see how we intervene and with what."
The figures released by the Government on Friday showed that, overall, 76% of primary school children reached or exceeded the national standard for reading, 72% for maths and 68% for writing.
Fairfax publications including The Dominion Post and The Press on Saturday published information on more than 1000 schools showing the percentage of children above, meeting, below or well below expected standards for reading, writing and maths.