By Angela Harrison
BBC News education reporter at the NAHT conference
Results from Sats tests are used to make school league tables
Head teachers will write to parents to explain why they support a boycott of Sats tests for 11-year-olds in England.
The National Association of Head Teachers (NAHT) will ballot its members over a boycott, a move also being taken by the National Union of Teachers.
The NAHT said it wanted to end the "tyranny of testing".
The Association of School and College Leaders said it was concerned a boycott could "harden attitudes" over the tests and make reform less likely.
NAHT general secretary Mick Brookes said the union's own research suggested overwhelming opposition to the tests.
He told BBC Radio 4's Today programme: "Practically everybody from the education establishment looked at these tests and saw that they narrowed the curriculum. It's a shallow measure.
"The secretary of state was saying our action will disrupt children's learning. We think exactly the opposite is true, that next year they will have an education that is uninterrupted by having to rehearse these tests.
"So it will be uncluttered, it'll be proper education, and what we want is sharper and more accurate information to go to our colleagues in the secondary sector so that the transition from Year 6 to Year 7 can be seamless."
Mr Brookes said the union's letter - for parents of Year 5 children who are due to take the tests next year - would go out "fairly soon".
Schools Secretary Ed Balls had urged heads not to opt for a ballot, shortly before the vote at the head teachers' annual conference.
He told delegates: "I know there are strong feelings here, I know you take very seriously your statutory duty, your role as role models for young people - you take very seriously your responsibility to do your best for children.
"But I have to say, I don't think the right thing, the responsible thing to do, is to boycott."
But he could not persuade the heads to abandon their plans, and 94% voted for a ballot.
Association of School and College Leaders general secretary John Dunford, said: "The secretary of state has said that the tests are not set in stone - there's an expert group reporting next week some time.
"It's the best possible time to reform these tests, and I think that the NAHT action might actually harden attitudes and mean that the tests are less likely to get reformed."
The Department for Children, Schools and Families has said previously that head teachers have a statutory duty to administer the tests, so would be breaking the law if they did not.
Mr Brookes said the NAHT would work with the government to try to find a solution, but if that was not possible, a ballot would be held in the autumn.
He told the conference civil disobedience sometimes served a noble purpose.
He said: "We do have a moral dilemma faced by others throughout history, when rules, regulations or regimes block the greater good.
"Without civil disobedience, women would not have the vote."
Many teachers dislike the tests and the league tables they go towards.
They say teachers are forced to over-focus on the tests, and they put both children and schools under too much pressure.
The other big union for classroom teachers in England, the NASUWT, does not support a boycott.
The NAHT says it represents 85% of primary school heads in England.
In the rest of the UK, children are tested but these are marked in school and not used for league tables.