Johnson, who resigned last month over the way May is negotiating Brexit, wrote in The Daily Telegraph this week that Denmark was wrong to ban the burqa, a head-to-toe cloak which conceals the face with a mesh or is worn in conjuction with the niqab - a face veil that leaves only the eyes exposed.
Shortly after the publication of his article on Monday, a source close to Mr Johnson said that it was "ridiculous" that his views should be under attack.
Prime Minister Theresa May joined in the chorus of calls for Johnson to apologize.
"I do think that we all have to be very careful about the language and terms we use". If a woman wants to wear a burqa, it's her right Mr. Boris Johnson.
There was no immediate sign that Johnson planned to back down. He resigned as foreign secretary in July, accusing May of killing "the Brexit dream" with her plan to seek close economic ties with the European Union after the United Kingdom leaves the bloc next year.
Some suspected Johnson's burka comments were meant to boost his appeal among right-wing members of the party.
The assistant secretary general of the Muslim Council of Britain, Miqdaad Versi, said Mr Johnson was "pandering to the far-right", while Labour MP David Lammy branded him a "pound-shop Donald Trump".
Cressida Dick said his remarks, made in this newspaper, do not meet the threshold for a criminal offence after she asked her officers to look into them on Wednesday evening. "Boris knew the effect and the impact that this kind of dog-whistle politics would have".
"The party chairman, the prime minister has the right to take the whip. that's the thing I'd like to see". The clothing has already been banned in France.