In an outspoken attack Chris Woodhead dismissed the tests, taken by every 7, 11 and 14-year-old, as unreliable and called for Government literacy and numeracy targets to be based on new standardised tests.
The TES revealed last month that Mr Woodhead believed changes to the tests had made year-on-year comparisons impossible and that schools were administering them "creatively" to get good results.
But Nicholas Tate, chief executive of the Qualifications and Curriculum Authority which runs the tests, has dismissed the criticisms.
In a letter to the TES which avoids any mention of Mr Woodhead, Dr Tate argues that standards are maintained by rigorous pre-testing of each year's questions.
The tests, taken in English, maths and science, are the basis for ambitious Government literacy and numeracy targets.
Seamus Hegarty, director of the National Foundation for Educational Research which developed some of the tests, said: "I emphatically reject Mr Woodhead's flawed critique.
"He is wrong when he says the tests are unreliable. He is wrong when he implies they are not standardised and he is wrong when he rejects the possibility of making comparisons across years.
"If the chief inspector's strictures were to be applied to his own annual reports, one wonders what weight would be attached to the numerous comparative judgment contained in them."
Platform 17, Letters 20, Leader 18