Many expect May to face a leadership challenge if faltering Brexit negotiations don't improve - and Johnson is likely to be a contender to replace her.
Cressida Dick said his remarks, made in this newspaper, do not meet the threshold for a criminal offence after she asked her officers to look into them on Wednesday evening.
Warsi responded in The Guardian, saying Johnson had used rightwing, "alt-right" language in criticising the appearance of the burqa, which contributes to a view that "Muslim women are fair game".
Sajjad Karim, the party's representative for North-West England, said Johnson's controversial comments had pushed the boundaries of acceptable political debate and as a result the party had to decide what future it wanted to embrace. "Boris knew the effect and the impact that this kind of dog-whistle politics would have". The clothing has already been banned in France.
Karim said that "Boris is playing to the gallery that exists at the right of the party" and by refusing to apologise was "positioning himself as the great defender of the right some believe they have to say whatever they like with no regard of consequences for others".
Palestinian rocket fire hits Israel, UN urges more Gaza fuel
The strikes came after two fighters from the military wing of Hamas, which rules Gaza, were killed by Israeli fire on Tuesday. Meanwhile, Israeli firefighters battled two fires caused by gas balloons that exploded when the homes were hit by rocket fire.
Meghan Markle’s Birthday Gifts: What She Can and Can’t Keep
He revealed: "If Meghan had much more makeup on, her face would have been the focus and not the gracefulness of her dress". Fast forward to now, and Meghan, 37, is in the midst of newlywed bliss after tying the knot to Prince Harry in May.