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Many Muslims have reacted angrily to Mr Straw's disclosure last week that he asks women to remove their veils when they attend weekly surgeries in his Blackburn constituency.
His comments drew both support and opposition from his party colleagues and provoked a heated debate on civil liberties and the possible impact on Britain's 1.6 million Muslim population.
Today, the Prime Minister added his voice to the debate by backing Mr Straw saying that it was important that issues surrounding religion and diversity were raised and that Mr Straw had done so in a sensible way.
"I don't think anyone is suggesting it's not a matter of personal choice in the end, for people to do what they want.
"But actually what Jack Straw was saying was perfectly sensible, which is that if we want to break down the barriers between people and between different cultures and religions, then it is important these issues are raised and discussed.
"I see nothing wrong with that and I think it is perfectly sensible if you raise it in a measured and considered way to have a proper public discussion about it, he told BBC Breakfast.
Mr Blair managed to sidestep a question as to whether in the same situation he would ask a Muslim woman to remove her veil and said: "It's a difficult, tricky debate to enter into, as we can see over the past few days, but he raised it in a very sensible and measured way."
Last week, Peter Hain, the Northern Ireland secretary, raised his opposition by saying he would never ask a woman to remove her veil however uncomfortable it made him feel. He said Mr Straw was entitled to his view, but that women had the right to dress as they chose.
But yesterday, John Prescott, the Deputy Prime Minister, said Mr Straw had been right to raise the issue, insisting it should not be a "no-go area for debate", but he also voiced concern that it could lead to "considerable difficulties" in terms of community relations.
Mr Straw, a former Foreign Secretary, said that the veil can be regarded as a visible statement of "separation and difference". Some Muslim scholars do not believe it is obligatory.
In his weekly column in the The Lancashire Telegraph he expressed concern that "wearing the full veil was bound to make better, positive relations between the two communities more difficult".
Mr Straw said he had been mulling over the issue ever since a veiled woman attended his surgery and said she was pleased to meet him face to face at last.
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