Mr Blunkett said that Mr Woodhead would continue to make a very important contribution towards raising classroom standards.
On Wednesday, Mr Woodhead may face further questioning when he appears before a committee of MPs which is investigating his Office for Standards in Education. Tomorrow, he will deliver his annual report on the state of schools.
Mr Woodhead accepted yesterday that he had made a mistake as he tried to reassure one member of his student-teacher audience and said that the views he had expressed were not his true views. He hoped that he would be judged on his contribution as chief inspector and not on a 30-second remark.
He told GMTV's Sunday Programme: "I readily admit I made a mistake. I can only apologise for giving the wrong impression, but I hope I can explain why I said what I did on that occasion."
During a question-and-answer session with 200 trainee teachers at Exeter University 11 days ago, one asked: "There has been a recent debate on teacher-pupil relationships of a certain nature. Do you think that any teacher who has been involved in such unpleasant action should have any place in the education system?"
In the course of his reply, Mr Woodhead suggested that the "messes" resulting from such relationships could be "educative". Legislation which would make relationships between teachers and under-18-year-olds a criminal offence and carry a jail sentence of up to two years is at present before Parliament.
Mr Woodhead told GMTV: "A student asked a question after the lecture I had given and I thought that there was a personal dimension to the question, that there may be a problem here and I tried to reassure that student in the answer I gave. And I readily admit that in trying to do that I overstepped the mark."
He believed that teachers were in a position of authority over pupils and it was important this was not abused.
He added: "I didn't for one moment think that the comments I made to that student would be leaked to The Independent newspaper and splashed over the pages of every other paper in the land."
Mr Blunkett said Mr Woodhead had given a very clear explanation of his remarks and had apologised. "He has obviously made - and I am confident he will continue to make - a very important contribution to the scrutiny of our schools and the drive to improve standards within them. Despite what Chris Woodhead has acknowledged to be an unfortunate incident, I believe it does not prevent him from continuing to do his job effectively."
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