Head teachers want the national curriculum tests that 14-year-olds in England have to sit to be scrapped.
The Association of School and College Leaders says young people will shortly have to take "functional skills" tests.
General secretary John Dunford says these cannot be tacked on to an already over-burdened national testing system.
In a TES education journal article he calls for a wider review than Lord Sutherland's ongoing inquiry into this year's marking problems.
With some results still not returned to schools, the delayed appeals process is being handled by England's National Assessment Agency (NAA) directly.
Contractor ETS is finishing this year's marking but its contract for future test delivery has been ended by mutual agreement.
Drawing parallels with the ill-fated steamship Titanic, Dr Dunford says: "Lord Sutherland has been asked to report on how the deckchairs might be rearranged, but what is needed is an investigation into the seaworthiness of the entire ship."
Publicity
Dr Dunford says: "This year's Sats marking crisis has been upsetting for thousands of young people and immensely frustrating for schools.
"But it will have been worth the pain if it leads to a major re-think of the testing regime, with the abolition of Key Stage 3 Sats and a different approach to Sats for 11-year-olds."
He said the publicity given to the crisis had brought to public attention two issues - the unsustainability of a testing system of such a size, and the cost.
"Can taxpayers really have contracted to pay £156m over five years for these tests?"
Functional skills tests, being introduced in 2010, would show all that was needed about how well young people could read, write, do maths and use computers.
That is what employers have been asking for. So 2010 is the year when Key Stage 3 tests should be abolished. We cannot have both. We do not need both."
Checks
A spokesman for the NAA said nearly all scripts had now been marked and schools would receive them back by 8 September.
The process of uploading results onto the website where schools can access them is continuing.
"This is being done as quickly as the capacity of the system allows and we expect all results to be available shortly," he said.
"Some further checks need to be carried out with schools before the results information is complete. This relates to cases such as pupils with marks for only one aspect of English - reading or writing - who may have been absent for one paper."
Latest figures show the following proportions of pupils' results are now accessible to schools online:
Key Stage 2:
English - 99.0%
Maths - 99.3%
Science - 99.4%
Key Stage 3:
English - 96.7%
Maths - 98.4%
Science - 97.9%
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