The outspoken Tory tried to calm anger at Number 10 yesterday, claiming his vow not to accept "Kosovo-style social cleansing" in the capital had been taken out of context.
But Employment Minister Ed Davey renewed government attacks on the mayor, accusing him of a flawed analysis of the changes and demanding he say sorry for "scaremongering".
The exchanges came amid reports higher-earning men will be required to disclose if their wives claim child benefit - with fines for non-compliance - in a bid to enforce another welfare cut.
It was reported yesterday that officials believed a move to strip higher-rate income taxpayers of the payout was "unenforceable" because mothers had no legal duty to declare partners' incomes.
Ministers derided that as "nonsense" amid Labour claims they had "added incompetence to unfairness" over the implementation of the controversial measure.
The Daily Telegraph said legislation would be used to force higher-rate taxpayers to declare - in tax returns or by reply to a letter - of any child benefit claim.
Payments would then be clawed back via their income tax codes.
Mr Johnson's intervention increased pressure on the Prime Minister, who is already facing opposition from Tory and Liberal Democrat backbenchers over the housing benefit shake-up.
There are claims that around 200,000 people could be driven out of areas with high rents as a result of the drive to reduce the cost of housing subsidies.
The mayor said he was in "detailed negotiations" with Work and Pensions Secretary Iain Duncan Smith about the proposals and said he would "emphatically resist" any such exodus.
"What we will not see and we will not accept is any kind of Kosovo-style social cleansing of London. On my watch, you are not going to see thousands of families evicted from the place where they have been living and have put down roots," he declared.
The comments drew a rare public rebuke from Number 10, which said David Cameron "doesn't agree with what Boris Johnson has said or indeed the way he said it".
Deputy Prime Minister Nick Clegg said he too "very strongly" disagreed with the comments and Business Secretary Vince Cable accused the mayor of using "inflammatory" language.
Asked about the issue on BBC1's Question Time, Mr Davey called for an apology from Mr Johnson and Labour MPs who have likened the consequences to social "cleansing".
"Chris and Boris Johnson should apologise. The language they are using is appalling, it is misleading, it is scaremongering and, worst of all, their analysis is clearly wrong," he said.
The planned moves include a £400-a-week housing benefit cap for four-bedroom homes and a 10% reduction for the long-term unemployed.
The Government estimates that 21,000 households will be affected by the cap on different size homes - 17,000 of them in London.
But more than 750,000 claimants could be affected by changes to the way Local Housing Allowance levels are calculated.
Labour had already seized on the issue with Opposition leader Ed Miliband seeking to assemble a cross-party coalition of opponents to the cuts by appealing to disgruntled Liberal Democrats.
"They are honourable people. They are in politics for the right reasons. I hope they will vote with their consciences when it comes to issues like housing benefit," he said.
Mr Cameron has made clear he intends to press ahead with the cuts, insisting it is not fair that claimants lived in properties many hard-working families could only "dream of".
Tory MP for the Cities of London and Westminster Mark Field said today he supported the housing benefit cap and would not have used the phrase "social cleansing".
He told BBC Radio 4's Today programme that about 5,000 households in his constituency would potentially be hit by the benefit cap, but he also believed many of their rents would be lowered.
He added: "I believe that the coalition are absolutely right to grasp the nettle on this and I support the cap."
Mr Field, asked about the Mayor's comments, said: "Social cleansing is not a phrase I would have used."
He said the experience of genuine victims of ethnic cleansing "can't really be compared with what's being proposed".
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