London Mayor Boris Johnson has said he will not accept "Kosovo-style social cleansing" of the capital due to a government cap on housing benefits.
Prime Minister David Cameron said he did not agree with Mr Johnson's view, or the words he had used.
The government has limited the amount paid in benefits according to the size of a property, including a cap of £400 a week on a four-bedroom house.
Mr Johnson's comments came as MPs were set to debate the issue in Parliament.
The Tory mayor said he was in talks with the Conservative-led coalition government to "mitigate the impact".
He told BBC London 94.9FM there was an "anomaly" in the housing benefit system which allows some landlords to make profit as "hard-working Londoners" pay.
Mr Johnson said: "The last thing we want to have in our city is a situation such as Paris where the less well-off are pushed out to the suburbs.
"I'll emphatically resist any attempt to recreate a London where the rich and poor cannot live together.
"People will always cry and say that I am at war with [the prime minister] David Cameron and try and get a headline out of that, but the fact is we are in detailed negotiations with the DWP, Iain Duncan Smith and his officials.
"What we will not see and we will not accept 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."
A spokesman for prime minister David Cameron said: "The prime minister does not agree with what Boris Johnson has said or indeed the way he said it. He thinks the policy is the right one."
Following the Spending Review, London Councils - which represents the capital's 32 boroughs - said up to 82,000 households could become homeless by next year due to the changes.
A spokesman said: "Boroughs are now talking to private landlords outside of the capital about procuring private properties in case they need to use them as temporary accommodation.
"This is of course a last resort. Boroughs don't want to move people into different homes outside of the capital - this causes disruption and comes at great cost.
"But unless the government takes on board the proper measures to prevent this housing crisis - like increasing a special hardship fund to help tenants who can't afford their rents - they might have no choice."
Labour mayoral candidate Ken Livingstone described this as "huge social cleansing out of central London", adding: "It's going to be a human tragedy on an amazing scale."
Business Secretary Vince Cable condemned Mr Johnson and said he had used "inflammatory language on a difficult and sensitive issue".
He added: "There is a genuine problem in the housing market in London - there isn't enough supply of housing, particularly affordable housing, private rents have been escalating, property prices have been escalating alongside."