In an interview with Daily Telegraph, Johnson said full-face veils should not be banned in Denmark but mentioned he found it "absolutely ridiculous" that women choose to "go around looking like letter boxes".
Prime Minister Theresa May joined in the chorus of calls for Johnson to apologize.
The party's chairman, Brandon Lewis, has received at least one written complaint about Johnson's conduct from the Muslim peer Lord Sheikh and has to decide whether to launch disciplinary proceedings against Johnson or not. May said she agreed with Lewis. "What starts as useful targets for "colourful political language" and the odd bit of toxic campaigning ends up in attacks on our streets".
The resignation solidified Johnson's position as a leader of the pro-Brexit wing of the Conservative Party, which is deeply divided over its attitude to the EU.
She added while many people have found the comments offensive, he "did not commit a criminal offence".
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".
Some suspected Johnson's burka comments were meant to boost his appeal among right-wing members of the party. "Boris knew the effect and the impact that this kind of dog-whistle politics would have".
Karim said that "Boris is playing to the gallery that exists at the right of the party" and by refusing to apologise was "positioning himself as the great defender of the right some believe they have to say whatever they like with no regard of consequences for others". The clothing has already been banned in France.