Mr Straw stood by his plea despite condemnation from Muslim leaders and many of his Blackburn constituents, while Downing Street stressed he was expressing a personal opinion that did not reflect Government policy.
Mr Straw had revealed he asks female visitors to his constituency surgeries to un-cover their faces, to improve "community relations".
Yesterday morning he went further, adding he would rather the veils were discarded completely.
He said communities were bound together by people's face-to-face relations in the street, but it was more difficult if people wore a veil.
He said: "I understand the concerns but I hope, however, there can be a mature debate about this.
"I come to this out of a profound commitment to equal rights for Muslim communities and an equal concern about adverse development about parallel communities."
Asked if he would rather the veils be discarded completely, Mr Straw said: "Yes."
But in Blackburn, where one in five people are Muslim, his comments were poorly received amid suspicion that Mr Straw was ad-vancing a bid for the Labour Party deputy leadership.
The Lancashire Council of Mosques said it was "deeply concerned" by his "very insensitive and unwise" statement, while the Islamic Human Rights Commission said Mr Straw was "selectively discriminating".
The campaigning organisation Muslim Public Affairs Committee accused the former Foreign Secretary of trivialising the "serious problem of segregation".
The Ramadhan Foundation, a Muslim youth organisation, questioned the "double standard" of not asking Sikhs to take off turbans or Jews to remove skull caps.
But Muslim peer Baroness Uddin said a "measured debate"was needed. "I think it's about human rights on both sides – Jack's right to say and the women's right to wear what they please."
Tory policy chief Oliver Letwin said it would be a "dangerous doctrine" to start telling people how to dress, while Liberal Democrat party chairman Simon Hughes dubbed the remarks "insensitive and surprising".
Bishop of Durham Tom Wright told GMTV he did not know what Mr Straw "was try-ing to get at" regarding a need for facial communication.
He said: "If they feel deeply embarrassed at the thought of revealing this private thing called their face to a stranger, then the last thing I want to do is embarrass them in that way."
n A Muslim woman aged 49 waiting at a Liverpool bus stop was "extremely shocked and upset" after a man snatched her head veil. The white man in his 60s shouted racial abuse at her. Police are treating it as a "hate crime".
william.green@ypn.co.uk



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