In a damage limitation exercise they wrote to parents warning them that the tables, which will be published on Tuesday, would create a false impression of what was actually happening in schools.
The National Association of Head Teachers claimed that the absence of only one or two pupils, who could have achieved level 4, would seriously distort the published results at key stage two.
It said results published on the basis of pupils who had reached a particular level made no allowance for special needs, how long children had been in school or the considerable achievement many had made to get to level 2 or 3.
David Hart, general secretary, said: "Not only will individual schools have cause to complain but the overall results will give those critical of the education service more ammunition to say that standards are not high enough. "
He said that the letters the NAHT was advising heads to send to parents about the tables were not meant to be "spoiling tactics".
"The Government's obsession with league tables, and its determination to publish them in a manner that will be wholly misleading in a significant number of cases, leaves us with no alternative. Schools stand a better chance of countering any negative publicity and of getting the Government's crude information in a proper context."
Two hundred West Country primary heads have taken out advertisements in regional papers to protest about the tables. They have paid Pounds 1,500 for the half-page ads, which say the league tables fail to reflect the special circumstances, progress made by children or the range of learning provided by the school.
Publication of the tables follows a government U-turn last February only 10 days after Gillian Shephard, the Education Secretary, said the opposite because the tests had not "fully bedded down".
Research into the tests carried out by 11-year-olds last summer, commissioned by the Association of Teachers and Lecturers, identified major flaws. It called for the tables to be scrapped until difficulties had been ironed out.
An independent evaluation by the University of Bath, published by the School Curriculum and Assessment Authority, found general satisfaction with the tests.
Doug McAvoy, general secretary of the National Union of Teachers, said: "We have no desire to limit the amount of information that goes to parents, but what we want is for that information to be adequate and relevant rather than superficial and a response to political pressure.
"After the election we would like to sit down with the new government and look at the opportunities for developing provision of information that will achieve that."
Troubled tables, page 5