Nick Clegg has admitted he has concerns about Muslim women who wear the full-face veil in classrooms or going through airport security, after a fellow Lib Dem minister suggest the state should ban the veil being imposed on young women by family pressure.
But the Deputy Prime Minister said he would oppose banning the veil, after Home Office Minister Jeremy Browne called for a national debate on the controversial issue.
The row sparked by a decision by Birmingham Metropolitan College to drop a ban on the wearing of full-face veils amid public protests.
A veiled Muslim woman perform prayers on Eid al-Fitr holiday marking the end of Ramadan
Clegg said: "I think there is a debate going on already in households and communities up and down the country.
"My own view, very strongly held, is that we shouldn't end up like other countries issuing edicts or laws from parliament telling people what they should or should not wear.
"This is a free country and people going about their own business should be free to wear what they wish. I think it is very un-British to start telling people what pieces of clothing they should wear.
"I think there are exceptions to that as far as the full veil is concerned - security at airports for instance. It is perfectly reasonable for us to say the full veil is clearly not appropriate there.
"And I think in the classroom, there is an issue of course about teachers being able to address their students in a way where they can address them face to face. I think it is quite difficult in the classroom to be able to do that."
Browne said on Sunday he was "instinctively uneasy" about restricting religious freedoms, but he added there may be a case to act to protect girls who were too young to decide for themselves whether they wished to wear the veil or not.
"There is genuine debate about whether girls should feel a compulsion to wear a veil when society deems children to be unable to express personal choices about other areas like buying alcohol, smoking or getting married.
"We should be very cautious about imposing religious conformity on a society which has always valued freedom of expression."
The Lib Dems are not the only party to voice concern. Conservative backbencher Dr Sarah Wollaston became embroiled in a Twitter spat with some followers, after she suggested feminists should oppose the face veil.
Writing for The Telegraph, she expanded on her views, saying: "It would be a perverse distortion of freedom if we knowingly allowed the restriction of communication in the very schools and colleges which should be equipping girls with skills for the modern world. We must not abandon our cultural belief that women should fully and equally participate in society.
"Once we accept the wearing of face coverings for pupils it will be hard to resist similar demands from teachers and what then of other public sector workers like doctors or nurses?
"The creeping acceptance of this form of sexual segregation has wider consequences for community cohesion as the niqab acts as a barrier to casual interaction and conversation."
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Mohammed Shafiq, chief executive of the Ramadhan Foundation, said in a statement: "This is another example of the double standards that are applied to Muslims in our country by some politicians.
"Whatever one's religion they should be free to practise it according to their own choices and any attempt by the Government to ban Muslim women will be strongly resisted by the Muslim community.
"We take great pride in the United Kingdom's values of individual freedom and freedom of religion and any attempt by illiberal male politicians to dictate to Muslim women what they should wear will be challenged.
He added: "I call on the Liberal Democrats to disown these illiberal comments from Jeremy Browne and ensure that no government with Lib Dem participation introduces this stupid Bill. If they fail to do this then they will face the consequences at the next general election from Muslim voters.
"We would expect these sorts of comments from the far right and authoritarian politicians and not from someone who allegedly believes in liberal values and freedom."