Boris Johnson is resisting demands that he apologise for his comments about Muslim women wearing burkas, branding his critics "ridiculous".
Conservative Party chairman Brandon Lewis ordered the former foreign secretary to apologise over a newspaper article in which the former foreign secretary compared women in the face-covering veils to bank robbers.
The call followed a hail of criticism for Mr Johnson's remarks, which were described as "offensive" by Foreign Office minister Alistair Burt and "bigotry" by former Tory chair Baroness Warsi.
A source close to Mr Johnson made clear he was not retracting his comments.
"It is ridiculous that these views are being attacked - we must not fall into the trap of shutting down the debate on difficult issues," said the source.
"We have to call it out. If we fail to speak up for liberal values then we are simply yielding ground to reactionaries and extremists."
Writing in the Daily Telegraph on Monday, Mr Johnson said he did not want Britain to follow European countries like Denmark which have banned the burka and niqab in public places.
But he described the burka as "ridiculous" and "weird" and said women wearing them looked like letter-boxes or bank robbers.
Mr Burt, who served under Mr Johnson until his resignation as foreign secretary last month, said he agreed with his former boss that the burka should not be banned.
But he told BBC Radio 4's Today programme: "I would never have made such a comment, I think there is a degree of offence in that, absolutely right."
And Lady Warsi accused Mr Johnson of adopting the "dog-whistle" tactics of former Donald Trump aide Steve Bannon in the hope of attracting support from right-wing Tories for an eventual leadership bid.
Repeating her call for an independent inquiry into Islamophobia in the Conservative Party, Lady Warsi told Channel 4 News: "Muslim women should not be a useful political battleground for Old Etonians.
"It is crass and it must stop, and it must be condemned by the leadership right from the Prime Minister down."
Mr Johnson has long campaigned for equal treatment for women in developing countries, especially the provision of education for girls.
His article stated that there was no requirement in the Koran for women to cover their faces, and attacked "bullying (and) oppressive" male-dominated governments which tried to force them to do so.
But in a message on Twitter, Mr Lewis said: "I agree with Alistair Burt. I have asked Boris Johnson to apologise."
Labour's equalities spokeswoman Naz Shah said an apology was not enough.
"Boris Johnson's comments weren't accidental, they were a calculated attack in a national newspaper, made weeks after he reportedly met with Steve Bannon," said Ms Shah.
"Clearly the Tory party has an issue with Islamophobia, but over 24 hours later the Prime Minister is still yet to say a word.
"Theresa May must condemn Boris Johnson's comments unequivocally and order an inquiry into Islamophobia in her party."
The Muslim Council of Britain said Mr Johnson's "intentional usage of the words" contained in his Daily Telegraph column appeared to be an attempt to "pander to the far right".
The MCB said Tories must now deliver the independent inquiry into Islamophobia in the party which it has been demanding. And it said that any inquiry must look into Mr Johnson's previous "incendiary remarks" that "Islam is the problem" and that "Islamophobia was a natural reaction".
The council also asked if Tory MP Nadine Dorries, who backed a ban on the burka, would be spoken to by the party chairman.
Mr Johnson's father, Stanley, came to his defence, telling ITV1's Good Morning Britain: "I think we are just picking holes here. I think people are whipping up a little mountain out of a molehill on this one, I really do."
And Ms Dorries said the former foreign secretary "did not go far enough".
"Any clothing a woman is forced to wear which hides both her beauty and her bruises should be banned and have no place in our liberal, progressive country," she said.
Shadow chancellor John McDonnell called for a campaign of resistance against the rise of the far-right, along the lines of the Anti-Nazi League.
Mr McDonnell lumped Mr Johnson in with Tommy Robinson and a group of vandals who stormed a left-wing bookshop as proof of the emergence of far-right forces in British society.
Ex-English Defence League leader Robinson became a cause celebre for elements of the political right around the world when he was jailed for 13 months for contempt of court after broadcasting footage on social media of people involved in a criminal trial.
He was released earlier this month after judges quashed the contempt finding, but warned he could still be returned to prison at a later hearing on the same allegations.
The Bookmarks bookshop in Bloomsbury, central London, said that "around a dozen mask-wearing fascists" attempted to intimidate staff and customers and to destroy books and other materials on Saturday.
Ukip suspended three party members understood to have been involved in the incident.
Mr McDonnell called for anti-racist campaigners to emulate the ANL, which was launched in response to the rise of the National Front in the 1970s and staged high-profile Rock Against Racism festivals featuring acts such as The Clash.
The shadow chancellor said: "With the scale of Tommy Robinson demonstrations, the storming of Bookmarks bookshop, and now Boris Johnson's Islamophobic comments, we can no longer ignore the rise of far-right politics in our society.
"Maybe it's time for an Anti-Nazi League-type cultural and political campaign to resist."