Schools could disrupt pupil tests across England by asking parents to send their children in late, head teachers say.
The NAHT says league tables 'demoralise schools'
The National Association of Head Teachers (NAHT) voted for an end to league tables for results achieved by 11 and 14-year-olds.
Union members were "sick to the back teeth" of government pressure, it said.
If less than two-thirds of pupils did tests, results would be invalid, general secretary Mick Brookes said.
Mr Brookes told the NAHT's annual conference in Harrogate that he wanted to persuade ministers to change the system without resorting to industrial action.
He added: "But I think we have permission from that conference to take action. Our members are sick to the back teeth of this constant downward pressure.
"They are giving me permission to push back."
It was still "early days" for developing a plan of action.
Parental support for head teachers would show a united front against tables, Mr Brookes said.
He said: "League tables just demoralise schools every year.
"When schools have been working hard to raise standards, it demoralises them when they are down at the bottom of the league tables."
Rona Tutt, a former NAHT president, said publishing information in this way was too "simplistic", adding: "Pupils are used as a data-feeder to be spewed out for league tables."
A spokesman for the Department for Education and Skills said: "Tests and performance tables are a non-negotiable part of our school reforms and an important way for parents to be informed of schools' and pupils' progress."