About 600,000 11-year-olds are preparing for Sats in May
Head teachers and teachers in England are threatening to boycott next year's national Sats tests in primary schools.
The National Association of Head Teachers and the NUT teaching union say the tests taken by seven and 11-year-olds damage children and schools.
They want assessments by teachers instead, and an end to league tables based on the 11-year-olds' results.
The government in England says the tests are important to parents and that a boycott would be "irresponsible".
The threat comes as hundreds of thousands of 11-year-olds are preparing to sit tests in maths, English and science in May.
The tests are marked externally and the results are used to make up school league tables.
In a joint campaign, the NAHT and the National Union of Teachers are to ask their members at their annual conferences this spring to vote on identical motions calling for a boycott.
They say there is widespread anger that the tests for 11-year-olds have not been scrapped.
Other unions have not joined the call.
The NAHT and NUT say the tests damage children's education, because teachers are forced to "teach to the test", narrowing the curriculum.
At the same time, teachers are "humiliated and demeaned" by the publication of the results in league tables, they say.
Last October Schools Secretary Ed Balls scrapped Sats tests for 14-year-olds in England after the fiasco over the marking of last years papers. But he has kept the tests for younger pupils.
The unions - who together represent the bulk of primary school staff - will give an ultimatum to the government in their conference motions.
They say unless they are listened to, they will ballot members on boycotting next year's Sats tests.
The ballot could take place this autumn.
'Unfair and unjust'
NAHT general secretary Mick Brookes said: "We've taken the case to the government, we think we've made the case, we've got most of the education community making the case with us, including governors and a considerable number of parents.
"We are not getting the message back we thought we would be getting about progress in changing Key Stage 2 tests in the near future."
NUT acting general secretary Christine Blower said: "Primary schools' patience in enduring the damage caused by the Key Stage 1 and Key Stage 2 tests has been stretched to the limit and beyond.
"It is particularly unfair and unjust that the government wants primary schools to continue with the very tests that it has decided to drop in secondary schools."
The unions say the tests should be replaced with a voluntary system based on teachers' assessments.
League tables should be scrapped, they say, and there should be a system of "sampling" to enable the government to measure how pupils are achieving over time.
Across the UK, school children are assessed but mainly by teachers, in schools.
The Westminster government has set up an expert group to advise on testing and assessment, which will report later in the spring. But it insists the tests are important.
A spokesman for the Department for Children, Schools and Families said: "These tests are important as they allow parents to see how their children and local schools are doing.
"Any attempt to boycott them could undermine this, and risk removing a basic right from parents.
"Heads have a statutory duty to administer them and any action to disrupt the smooth running of national tests would be a disappointing and irresponsible step that would only serve to cause inconvenience and disruption to teachers, schools and parents."
Schools Secretary Ed Balls told BBC News it was too early to say whether he would take action against heads boycotting the tests.
New approaches - based on tests assessing whether children meet a particular national curriculum level - were being piloted, he added.