The National Union of Teachers' conference heard warnings that schools had become "exam factories".
Delegates criticised "chaotic" changes to primary assessment and voted for a ballot to boycott tests taken by seven and 11 year olds and baseline tests.
NUT leader Christine Blower said the union would consider a ballot to boycott tests in summer 2017. She said the union was also calling on the education secretary to cancel this year's Sats tests.
Delegates particularly criticised the baseline tests being introduced in Reception classes.
Also Read
The test is intended to provide a starting point against which to measure future progress through primary schools. But Sara Tomlinson from Lambeth said that such tests were "not what the first six weeks of school should be about".
She said that children should be learning social skills and "not just sitting down and repeating words like parrots".
The conference motion condemned the "chaotic and wholly unacceptable way" in how changes to primary assessment have been managed.
There have been particular warnings about the spelling, punctuation and grammar element of primary tests, with claims that they are unrealistically difficult for the age group, the BBC reported.
Delegates attacking a "testing culture" have warned that the primary assessment plans will mean there would be tests in Reception, Year 1, Year 2 and Year 6.
There are warnings from teachers that an excessive emphasis on testing narrows the curriculum and reduces creativity, with the pressure of school league tables taking precedence over the needs of individual pupils. There are also claims that tests can be stressful for pupils.
A spokeswoman for the Department for Education said that parents had a right to expect that there should be tests to show that children leave primary school with the right skills in maths and literacy.
"We want to see all children pushed to reach their potential. In order to do that, and to recognise the achievements of schools in the most challenging areas, we want to measure the progress that all pupils make as well as their overall attainment.
"It is disappointing to see that the NUT are taking this approach, which would disrupt children's education, rather than working with us constructively as other unions have," the spokeswoman said.