However, Education Minister Anne Tolley has called the move "completely irresponsible".
The suggestion to withhold information was made to more than 180 parents and boards of trustees members at a Canterbury Primary Principals' Association meeting in Christchurch this week.
Members of the Canterbury association gave examples of the perceived flaws in the system which they say renders its data meaningless and gives an inaccurate and incomplete picture of how children and schools are doing.
Canterbury president Denise Torrey also told those present she was disappointed Mrs Tolley had appeared to dismiss principals' concerns.
Otago Primary Principals' Association president Jenny Clarke said many boards and experienced principals across Otago had started to implement the standards, only to find there were some concerning discrepancies.
As a result, they now supported national action to bring about a revision of the system and highlight to parents the shortcomings and flaws of the hastily constructed and untrialled initiative, she said.
"Principals do not think this policy is exclusively about helping children. It has already led to some confusing and unfair reporting to parents, and it is unlikely to advance our world class education system in the way the Government intends.
"Principals have a professional and ethical responsibility to alert the education minister and parents to their concerns."
She said the Otago association would meet soon to discuss whether it would follow Canterbury's idea of advising boards of trustees to hold off on reporting National Standards.
Mrs Tolley said if boards of trustees failed to report National Standards information, they would be breaking the law.
"This organisation [CPPA], which we must now view as totally political, is completely out of touch with public opinion, and has reverted to yet another scaremongering campaign, targeting parents and children.
"If this organisation devoted as much time to helping our students as it does to silly political games, then almost one in five of our students wouldn't be leaving school without the skills they need in reading, writing and maths."
Mrs Tolley said it was more politicking from the New Zealand Principals' Federation, which had been against National Standards since the policy was first announced.
"I've met with them, listened to them, watched a presentation on the standards, and repeatedly agreed to work constructively to ensure the success of our goal, which is to lift student achievement.
"In return, the [federation] has refused to make any information available to me to get advice on, they have demanded moratoriums and issued threats of `a long, dirty and expensive fight'."
In the past 18 months, the federation had brought nothing positive to the table, she said.
"I can only conclude this is all about egos, and nothing to do with lifting achievement for our children.
"The majority of schools are getting on with implementing the standards. It's time NZPF moved on from last century's arguments."
