The former foreign secretary has so far defied mounting calls for him to apologize for the comments.
May said the remarks "clearly caused offence" as she told him to say sorry.
She said: "Some of the terms Boris used describing people's appearance obviously have offended.
"So I agree with Brandon Lewis.
"What's important is do we believe people should have the right to practice their religion and, in the case of women and the burka and niqab, to choose how they dress.
"I believe women should be able to choose how they dress."
A source close to the former foreign secretary told Sky News it was "ridiculous" his views were being "attacked".
They said Britain must not "fall into the trap of shutting down the debate on serious issues".
"We have to call it out," the source added. "If we fail to speak up for liberal values then we are simply yielding ground to reactionaries and extremists."
The controversy sprung from a piece Johnson wrote for the Daily Telegraph on Monday, in which he argued against following Denmark's lead in banning the burka.
But he made several comparisons between the covering worn by some women, saying it made them look like a "bank robber" or a "letter box".
Mr Johnson also revealed he would "feel entitled" to ask a woman wearing the burka to remove it if she came to his constituency office.
He concluded: "In Britain today there is only a tiny, tiny minority of women who wear these odd bits of headgear.
"One day, I am sure, they will go."
The comment sparked a backlash from senior Conservatives, including Brandon Lewis, the party's chair.
He revealed on Tuesday he had asked Johnson to apologize.
Baroness Warsi, the first Muslim cabinet minister and a former Tory party vice-chair, also told Sky News that Johnson was using the issue as a "political football" to "increase his poll ratings".
"I hope he will be disciplined but I'm not holding my breath."
She said: "Mr Johnson is making yet another leadership bid, and he will say and do whatever needs to be said and done to make that as successful as he can.
"I hope he will be disciplined but I'm not holding my breath.
"Sadly this is not the first time that such comments have been made within my party."
Baroness Warsi added that when Conservative politicians made "crass" comments about British Muslims, it "doesn't diminish their political status, it actually increases their political success".
Conservative MP Nadine Dories responded on Twitter: "Any clothing a woman is forced to wear which hides both her beauty and her bruises should be banned."
She added: "Boris didn't go far enough."
Source: Sky News