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".
Mohammed Sheikh, founder of the Conservative Muslim Forum, said Johnson's article had been "totally out of order".
London's Met Police Commissioner has been accused of "diverting precious resources" after she revealed she asked her hate crime experts to look into whether Boris Johnson's comments on the burka constitute a hate crime. It was the wrong language to use.
Latin-spouting, tousle-headed Johnson is a former mayor of London and one of Britain's best-known politicians.
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. Some suspected Johnson's burqa comments were meant to boost his appeal among right-wing members of the party.
Baroness Warsi repeated her calls for an investigation into Islamophobia within the Conservative party in a piece in the Guardian, and noted there had been a 26% rise in hate crimes against Muslims a year ago, according to figures from monitoring group Tell Mama.
"I believe women should be able to choose how they dress", said May.
"If you say that it is weird and bullying to expect women to cover their faces, then I totally agree - and I would add that I can find no scriptural authority for the practice in the Koran". The clothing has already been banned in France.