In an interview on BBCBreakfast Mr Clarke said, 'We are not getting rid of them, but we are open to looking at ways of making the tests less stressful than they appear to be.'
A Department for Education and Skills spokeswoman later confirmed that the Government was ready to listen to concerns about the pressure of the tests.
'We are happy to engage in a debate about content and process, but testing is central to raise standards,' she said, amid signs that some parents are insisting that their children are not made to do the tests.
Diane Rich, national professional officer of Early Education, said she had been inundated with calls from parents concerned about the pressure on their children, with some withdrawing them from the SATs. She told of one parent who did not want her seven-year-old daughter to do the SATs, who was given ten minutes' notice by the headteacher to come and collect her from school or she would be forced to sit the tests.
'This was despite the parent making it clear in advance that she did not want her daughter to do the tests. She was then told by the head to keep her off school for three weeks until the testing process was completed.
This parent was distraught. I am hearing of more and more incidents like this,' Mrs Rich said.
'What would the scenario be if all parents chose to take the same action as this parent? What, in particular, would happen if all parents of bright children withdrew them from the SATs? This would surely affect league tables,' she added.
Early Education, which supports the abolition of SATs at Key Stage 1, insisted that ending tests for six- and seven-year- olds would not only bring England into line with Wales and Northern Ireland but would also 'raise attainment by 11'. It warned that SATs at Key Stage 1 were having an adverse impact on children and teachers and would jeopardise implementation of the Foundation Stage.
Early Education said that it believes that teacher assessment, with inbuilt moderation, is more reliable than SATs, effective teaching time is lost preparing for and administering the tests, the cost of SATs would be more productive if spent on supporting learning and teaching, and SATs offer no tangible benefits to the child, narrowing the curriculum, turning them off learning and inhibiting their future learning potential.