Russell Hobby closed the National Association of Head Teachers’ conference by calling for a fundamental review of assessment of pupils.
Pupils should only be formally assessed at the start and end of primary school, he said.
Plans for Reception tests were axed last month before being re-introduced.
The government had approved three separate baseline tests, which were to be used to measure the progress of pupils from when they start primary school to when they leave at age 11.
Thousands of schools had adopted one of the three, only to be told they were not going to be used to measure progress as had been intended.
Ministers say they are committed to a new baseline test and are working on new plans for this.
Teachers have also been grappling with a new curriculum, new tests and assessments, and complained of a lack of information.
Heads expressed their anger with the situation on Saturday when they heckled and jeered Education Secretary Nicky Morgan.
Mr Hobby told delegates in Birmingham: “We cannot and will not endure another year of chaos.
“School leaders cannot do their duty to children under these circumstances.”
He also called for a new approach to assessment of pupil’s progress in primary schools.
Currently pupils are assessed formally through national tests at age seven and 11.
He said: “If you are going to measure progress you need a start measure and an end measure.
“And you should start at the beginning of school, not in the middle, missing out the most important years of a child’s education.”
But any Reception baseline test would have to be “one that works” and “not the mess that we’ve seen this year”, he said.
He argued that statutory assessments for Year 2 pupils should be scrapped: “We cannot have two high-stake tests for young children.”