Labour has called on Badenoch to sack Timothy over the comments, with party chair Anna Turley branding them “utterly appalling”.
Khan hit back in a newspaper interview, saying that Trafalgar Square had hosted public events for Christians, Hindus and Sikhs.
“What is so objectionable to the Conservative Party about Muslims celebrating their religion in the way that we do?” he added.
But speaking at an event to launch her party’s campaign for May’s local elections in England, Badenoch said her “fantastic” frontbench colleague Nick Timothy had been trying to make a point about the “norms of British culture”.
Claiming that women at the event had been “pushed to the back,” she said the gathering had been “exclusionary”.
“It is about how religion is expressed in a shared public space, and whether those expressions fit within the norms of British culture, ” she added.
In a BBC interview after the event, she went on to add: “I think that we need to look at exactly why and how it happened in that space.
“We already have loads of planning rules to say what events can go on, and which ones cannot. I don’t think that that was one that should have gone on. So let’s look at the rules that allowed that to happen.”
Asked why she had mentioned the place of women when this had not featured in Timothy’s original criticism of the event, she replied: “My position has been very clear, and very consistent.
“We need to bring back British values. We need to make sure that we enforce British identity.”