Principals say newspapers should never have published individual schools' results in the national standards in reading, writing and maths.
They say the figures are demoralising for teachers in poor areas, and will fuel pointless competition.
Principals says the results have been made public in a manner that encourages comparisons between schools.
They say that is disappointing because schools' use of the standards is not yet consistent and comparisons are likely to be wrong.
They also worry schools in poor communities will appear to be doing badly even if they are doing great work with children from disadvantaged backgrounds.
The newspapers published the results of more than 1,000 primary and intermediate schools, but the Ministry of Education will publish figures for nearly all the 2,000 schools using the standards on Friday.
The principal of a low-decile school says there was no need for National Standards results to be published in league tables.
Geoff Lovegrove, of Lytton Street School in Manawatu, says in many cases, schools gave parents better information before the introduction of national standards.
"Maybe some schools didn't, and this is where we get the sledgehammer and the nut equation, where if a few schools were not performing well, then address those ones. And this is where ERO can play its part, if they are identifying a school that's not performing well, then put some help and support into those schools."
Mr Lovegrove describes the national standards testing as puerile.
The president of both the Waikato and Catholic primary principals associations says publication of schools' national standards figures could unfairly damage schools in poor communities.
John Coulam says the results do not show how much progress schools make with their students and that could harm low decile schools.
"There's a real danger in taking data that's raw and reading into it without the understanding and the background of what's going on, of creating schools that are hard to staff, of creating some schools that are winners and losers and as principals we don't support that at all.
"We believe all our colleagues work hard in schools to make a difference with the resources that they have available."
He says people should not put too much emphasis on the results.
