Head teachers are calling on the education secretary to stop the publication of this year's primary school results in England.
They warn of "serious mistakes" in the introduction of changes to tests and say results are too "unpredictable".
This year's primary tests also saw a series of leaks and cancellations.
But the Department for Education said its reforms would "help ensure all children leave primary school having mastered the basics".
Leaders of the National Association of Head Teachers have written an open letter to Education Secretary Nicky Morgan urging her to cancel the public use of any data from this year's primary tests.
It would mean there would be no primary school league tables, based on the tests taken by 10 and 11 year olds.
The head teachers' union says that individual pupils should be given their results, with warnings to parents about concerns about their reliability, but the results were not robust enough to be used to make comparisons between schools.
Heads are complaining about "inadequate" time to prepare for changes, "obscure guidance" and "massive variations" in how schools approached the tests.
They say that the outcomes of the tests are likely to be so "skewed" that "comparisons between schools become very risky".
The heads' union says ministers need to address the "growing disquiet about assessment".
There were further difficulties this year when part of the English test for seven year olds had to be cancelled because questions had been published on a Department for Education website.
There were then claims of a "rogue marker" trying to disrupt the exams, when part of the English paper for 11 year olds was put on to a password-protected website the day before it was due to be taken.
Baseline tests for reception pupils also had to be scrapped, when it was found that the different types of tests being used did not produce consistent results.
A Department for Education spokesman said: "We have reformed the primary curriculum to help ensure all children leave primary school having mastered the basics, and the support and hard work of teachers is key to making this happen.
"We are determined to get this right and remain committed to working with teachers and head teachers as we continue with our primary assessment reform. We will respond to this letter in due course."