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By Thomas Mackintosh
BBC News
Sadiq Khan has described remarks by the former Tory deputy chairman as "pouring fuel on the fire of anti-Muslim hatred".
Lee Anderson told GB News "Islamists" had "got control" of the mayor of London.
His words, which follow pro-Palestinian protests outside Parliament, have been condemned by some Conservatives.
But Mr Khan criticised Rishi Sunak and his Cabinet for what he called a "deafening silence".
On Friday, Mr Anderson told GB News: "I don't actually believe that the Islamists have got control of our country, but what I do believe is they've got control of Khan and they've got control of London… He's actually given our capital city away to his mates."
The Ashfield MP's remarks prompted criticism from Labour and some Conservatives - including former chancellor Sir Sajid Javid who reposted the video of Mr Anderson making the comments and wrote "a ridiculous thing to say".
In response, Mr Khan described Mr Anderson's comments as "Islamophobic, anti-Muslim and racist".
"These comments pour fuel on the fire of anti-Muslim hatred," Mr Khan said.
"I'm afraid the deafening silence from Rishi Sunak and from the Cabinet is condoning this racism and confirms to many people across the country there is a hierarchy when it comes to racism in this country.
"I am unclear why Rishi Sunak and members of his Cabinet aren't calling this out and condemning this."
Earlier on Saturday, Labour called for Mr Anderson to lose the party whip - which would essentially expel him from his party in Parliament.
Until January Mr Anderson served as one of the deputy chairmen of the Conservative Party, but he resigned so he could rebel against the government over the Rwanda vote.
His comments followed an article by former home secretary Suella Braverman in the Daily Telegraph, in which she said "the truth is that the Islamists, the extremists and the anti-Semites are in charge now".
A Tory source earlier told the BBC: "Lee was simply making the point that the mayor, in his capacity as police and crime commissioner for London, has abjectly failed to get a grip on the appalling Islamist marches we have seen in London recently."
But Neil Garratt, leader of Conservatives at City Hall, said he had "no shortage of criticisms of Mayor Khan" but added "he is not an Islamist, he is not in the pockets of Islamists, and I completely disagree with anyone who says otherwise".
The BBC has approached Mr Anderson and the government for comment.