Ms Faifi, who wears niqab, a veil which leaves the eyes uncovered, said she could "empathise" with people who find it hard to connect with women whose full faces they cannot see.
Conservative Party chairman Brandon Lewis called on him to say sorry after a flurry of criticism, supported by the Prime Minister.
Sahar al-Faifi, who has covered her face since she was 14, said that negative rhetoric is making Muslim women feel "unsafe".
Lord Sheikh, the president of the Conservative Muslim Forum, said "severe action" should be taken against Johnson, including the withdrawal of the party whip.
Mrs May said: 'I do think that we all have to be very careful about the language and terms we use. "And some of the terms Boris used describing people's appearance obviously have offended", she said.
But the former top diplomat, who has a reputation for causing controversy and quit May's cabinet last month in protest at her Brexit plan, refused to back down.
Defense lawyer: Gates to testify next in Manafort’s trial
Kilimnik is a Russian-Ukrainian political consultant who was indicted in June on charges stemming from the Mueller probe. Manafort faces charges of bank fraud and tax evasion that could put him in prison for the rest of his life.
And Munira Mirza, a former deputy mayor of London, said: "There is a political fight here".
Johnson resigned as Foreign Secretary in July, accusing Theresa 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. Why not? He's not a super human being, he's a member of the party.
She further said that a woman is not answerable to anyone if they wish to wear a burqa.
"You're forgetting that there's a human being behind it", she said on ITV's Good Morning Britain. "Boris knew the effect and the impact that this kind of dog-whistle politics would have".
The Austrian parliament adopted a legal ban on face-covering clothing in public spaces in 2017.
Junior foreign minister Alistair Burt told the BBC: "I would never have made such a comment, I think there is a degree of offense in that, absolutely right".