The former foreign secretary’s likening of women who wear the Muslim face veil to letterboxes and bank robbers prompted growing outrage from senior Conservatives.
Culture Secretary Jeremy Wright and leader of the Scottish Conservatives Ruth Davidson joined the Prime Minister Theresa May in suggesting Johnson’s comments, made in a column for the Daily Telegraph, crossed a line.
But Johnson’s supporters claimed he was being targeted in attempt to dampen a future leadership challenge.
Wright said that politicians must choose their language with care when discussing issues such as the burka.
“When you are discussing a subject such as this, then I think describing it as people looking like letterboxes isn’t helpful,” he told BBC Radio 4′s Today programme.
Davidson, however, went further, saying Johnson’s comments had been “gratuitously offensive” and that he needed to apologise.
“I think that this wasn’t an off-the-cuff slip, he wrote a column, he knew exactly what he was doing and I think it crossed from being provocative and starting a debate and actually it became rude and gratuitous,” she said.
Meanwhile Tory MP Anna Soubry suggested that the furore cast light on Johnson’s lack of support as a potential future leader of the party, raising the prospect of a split.
“I believe many One Nation Tories would not stay in the Conservative Party should [Boris Johnson] become leader,” she wrote on Twitter.
“I also believe Dominic speaks for many millions of people who despair at the state of both main parties.”
Soubry lent her support to former Conservative minister Dominic Grieve who said that he would leave the party should Johnson become leader.
“If he were to become leader of the party, I for one wouldn’t be in it. I don’t regard him as a fit and proper person to lead a political party and certainly not the Conservative party,” he said.
Meanwhile Tory peer and president of the Conservative Muslim Forum, Lord Sheikh, said on Wednesday that Johnson should be kicked out of the party altogether.
“We should consider taking severe action against him. If we need to take the whip off, let’s do it,” he told Sky News.
Sheikh’s words followed Lord Pickles, the former communities secretary, who said earlier that Johnson should face disciplinary action should he not back down and apologise.
Johnson, who is said to be on a foreign holiday, has not spoken out since his column was published on Monday.
But Conservative MP Nadine Dorries said she does not believe his views on women wearing burkas are offensive.
“I believe it was an accurate description, it was one that many people have used,” she said.
“I do not think it was offensive. What people find offensive is women being forced to cover up in public places.
“There is no place in our society for women who are forced to cover up from head to toe.”