The man who introduced school tests - former Conservative education secretary Kenneth Clarke - says seven-year-olds are stressed by them only because of "over-concerned adults".
And the organisation which administers the national curriculum tests says its evidence is that children do not find them stressful - contrary to what some parents and teachers are saying.
On Wednesday the present Education Secretary, David Blunkett, said he would consider changing the testing arrangements - if it could be shown that stress was widespread.
It was made clear later by his department that the tests should be carried out so that they did not put young children under undue pressure.
The Department for Education says seven-year-olds should be tested in normal classroom conditions and should hardly be aware of what is happening.
'Not a normal lesson'
On Monday a parent and former primary school teacher in Somerset, Penny Holmes, said she intended keeping her seven-year-old off school during May when the tests are carried out.
She complained of unnecessary stress on children so young - and that the tests were being used politically to show that standards were rising on a narrow curriculum.
Other parents and teachers have since contacted the BBC.
Read your views on testing seven-year-olds.
Teacher Catherine Emmitt thinks Mr Blunkett is not aware of the guidance schools are given regarding the tests.
"We have a script to read the instructions to the children. They mustn't talk to each other, they must be undisturbed, work individually, and in order to do this in an ordinary classroom children have to sit separately from each other, be quiet not talk to each other as they would normally do in an infant classroom, and I would call those test conditions," she told BBC Radio 4's Today programme.
The pressure is even greater at Key Stage 2 - when the results of children's tests in their final year of primary school are published annually and form the basis of school performance tables in England.
"I feel quite nervous because I want to do well and I don't want to let down my teacher," said 10-year-old Charlotte Dove.
"It puts pressure on the class because everyone's really worried about whether they are going to do well or not."
Her mother Jan said children were coming home from school knowing they had eight days after the Easter holiday before they were to take the tests.
"If the children are coming home saying that it's really highlighting how much they realise is riding on them," she said.
'Necessary measure'
Kenneth Clarke was education secretary in the Tory government which brought in the tests in 1991.
"I think we've heard some rather over-concerned adults and some examples of rather over-concerned adult behaviour," he said.
The tests did not harm seven-year-old children and were necessary to measure what progress they were making.
"Until we had the tests ... parents had no information at all about the progress being made by children at school.
"And the huge variations in performance that existed, the huge variations in quality of education in different schools was just taken for granted."
It would he said be "a disaster" to reverse these educational reforms.
'Ninety per cent stress-free'
The Qualifications and Curriculum Authority (QCA) administers the national curriculum tests for seven, 11 and 14-year-olds in school Key Stages 1, 2 and 3.
It says most pressure is put upon children by their parents.
Gail Cowmeadow, the QCA's Key Stage 1 assessment team leader, said over 90% of teachers thought the tests did not stress their pupils.
"Generally speaking they give them a positive rating for lack of stress," she said.
"However parents have become more aware of the tests and I think sometimes they are putting pressure on children, they don't know they are doing it, but they are putting pressure."
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