0905 GMT July 16, 2019
Heads gathering for the union's annual conference in Birmingham are urging the government to work with them to set up a new assessment system for next year.
NAHT head Russell Hobby said primary tests no longer gave parents reliable information on children's progress.
Tests allow teachers to spot when pupils need more help, say ministers.
The NAHT highlighted issues such as a lack of time to implement the new primary curriculum and its ‘inappropriate content’, a lack of clarity on standards and contradictory guidelines plus the late publication of materials.
It also highlighted the accidental publication of the content of the spelling, punctuation and grammar test and the cancellation of this year's planned baseline test for pupils in Reception following unsuccessful trials.
Speaking ahead of the conference, Hobby said: "Testing has a role to play in the assessment of children, but the poorly designed tests and last minute-changes we have seen this year do not add value to teaching.
"Increasingly, parents and teachers agree that high-stakes statutory tests like Sats can actually make it harder to find out what children are really learning and to improve their education.
"Our conversations with parents show that they want tests and assessments which help schools understand their children ― on a regular basis with lower stakes ― rather than what are fast becoming high-profile high-pressure exams."
The incoming NAHT president, Kim Johnson, is to highlight, in his speech, how pressures being placed on children and young people are having an impact on their mental health.
And he will say educational funding is being used to prop up social care and health services in schools.
"The impact on our budgets is significant, yet we daily make decisions that must address well-being, basic food and clothing needs, and medical care to give some children the same start to the day that others take for granted," he will add.
The head teachers' union also plans to debate issues such as forced academization, assessment and British values in schools, over the weekend.