The former foreign secretary came under fire after writing that Muslim women who wear face veils looked like “letterboxes” and “bank robbers” in his column last week.
However, this week he chose to turn his attention to proposals to encourage house building – despite a week of intense debate between those defending him and those outraged by his remarks.
Mr Johnson instead called for cuts to “absurdly high” stamp duty and warned of construction firms reducing the supply of new homes by “land-banking”.
On Sunday, the politician refused to answer reporters’ questions about his remarks on the burka as he returned to his Oxfordshire home following a holiday in Italy. He did, however, emerge from his house to offer them cups of tea.
He is yet to respond to allegations of Islamophobia as well as Theresa May’s demands for an apology.
Former aide to Donald Trump Steve Bannon is among those defending Mr Johnson. He said the former London mayor had “nothing to apologise for” and that he should not “bow at the altar of political correctness”.
The Republican strategist pointed out that Mr Johnson’s column argued against banning full-face veils, as Denmark has done.
Mr Bannon told the Sunday Times: “His entire argument revolves around not wanting to ban the burka, but arguing that he agrees that it’s an oppressive garment and that there is no scriptural basis for it in the Koran, which is true. I think the substance got lost because of his throwaway line.”
The comments come after Mr Johnson’s father Stanley Johnson said people should be “grateful” to his son for putting the issue of banning the burka “on the table”.
He told Sky News that much of the criticism was “synthetic indignation” that had been “whipped up” by his opponents.
However, Conservative chair Brandon Lewis instructed an independent panel to investigate Mr Johnson following complaints his comments breached the Tories’ code of conduct.
Tory MP Andrew Bridgen, a supporter of the former cabinet minister, said there would be “open warfare” in the party if Mr Johnson was severely disciplined over his burka comments.
He issued the warning in the event the former foreign secretary is suspended in such a way that he cannot not take part in a future leadership contest.
Mr Bridgen told the Sunday Express: “If Boris is suspended it will be open warfare in the Conservative Party. If Theresa May dares engineer a leadership contest while Boris is suspended it will be World War Three.”
But former close aide to David Cameron, Lord (Andrew) Cooper, accused Mr Johnson on Saturday of “casual racism” and “courting of fascism”.
“He will advocate literally anything to play to the crowd of the moment. His career is a saga of moral emptiness and lies; pathetic, weak and needy; the opposite of strong,” Lord Cooper said.
The Muslim Council of Britain (MCB) said on Saturday that Conservative MPs’ support for Mr Johnson over his comments women wearing the burka had “shone a light on the underbelly of Islamophobia” within the party.