Ruth Davidson, the Scottish Tory leader, also tore into him for "gratuitously offensive" comments claiming women in burkas looked like letterboxes and bank robbers.
Met Police boss Cressida Dick, said despite reports being made against Boris, what he said does not "meet the bar" to be considered criminal.
A Sky News poll found that 45% of voters thought he should apologise, while 48% thought he should not.
The Belgian parliament passed a bill in 2010 to ban any clothing that would obscure the identity of the wearer in public places.
She said that her group, which works with marginalised women, had already taken three calls in the last two days from hijab-wearing women who reported being called "letter boxes".
Parliament agreed a ban on face-covering garments for soldiers, state workers auto and truck drivers in 2017.
The new law went into effect August 1.
The row has highlighted deep divisions within the party, with former attorney general Dominic Grieve saying he would quit the Tories if Mr Johnson became leader.
"I don't regard him as a fit and proper person to lead a political party and certainly not the Conservative Party".
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Warsi said Johnson was hoping to attract support from right-wing Conservatives for an eventual leadership bid, and called for an independent inquiry into Islamophobia in the party.
Latin-spouting, tousle-headed Johnson is a former mayor of London and one of Britain's best-known politicians.
And an imam who has previously criticised the burka said Mr Johnson should not "apologise for telling the truth".
"I do think that we all have to be very careful about the language and terms we use".
"You're forgetting that there's a human being behind it", she said on ITV's Good Morning Britain.
The BBC News interview, broadcast on a television in the waiting area, featured a Muslim woman in a niqab.
"The way she described it, it wasn't just Islamophobic".
"This inflammatory language will in fact motivate and fuel hate crimes, particularly towards visibly Muslim women who wear the veil or the hijab", Sajda Mughal, who runs the JAN Trust charity, told the Thomson Reuters Foundation.
"As an organisation championing the rights of Muslim women, we are all too familiar with the ways in which this "natural reaction" manifests itself: a woman who was attacked, punched and had her headscarf ripped off, and another who had a bottle smashed over her head in a bus, both in Glasgow this year".
She said: "Now, literally people are messaging me on Twitter and calling me a "letterbox".