Margaret Hodge today defended her call for British families to be given housing priority over immigrants as critics claimed she was at risk of allowing the far-right BNP to dictate government policy.
The industry and regions minister acknowledged that the issue was "difficult and contentious" but said that she hoped to engage in a "civilised and constructive dialogue".
Mrs Hodge spoke out after her comments at the weekend prompted outrage from politicians of all parties.
Earlier today, Ken Livingstone, the mayor of London, warned that her outburst would be "catastrophic for community relations", while Labour MP Diane Abbott tabled a Commons motion condemning her remarks.
But this afternoon Mrs Hodge issued a statement saying: "I set out to ask some difficult questions on the tension between 'entitlement' and 'need' in the allocation of social housing.
"I want us to debate openly an issue that many people talk about privately.
"I, of course, accept the need for more social housing and did so in the article. However there will always have to be rules to ration what will always be a finite resource.
"These rules need to be transparent and they need to be perceived as fair. The idea that this debate is about scapegoating immigrants is simply wrong."
However, Mrs Hodge avoided repeating the remarks she made at the weekend that caused so much controversy: "We should look at policies where the legitimate sense of entitlement felt by the indigenous family overrides the legitimate need demonstrated by the new migrants."
David Cameron, the Conservative leader, responded by cautioning MPs against "pouring out of their surgeries" and adding to the debate on immigration after listening to complaints from constituents which could be based upon rumours and inaccuracies.
And earlier today Ms Abbott insisted that the current housing crisis would not be solved by "scapegoating homeless families on the basis of race, ethnicity or national origin".
"Mrs Hodge has implied that at the moment immigrants receive some sort of special treatment for social housing; that is simply not true," she said.
"The problem with housing does not come from immigrants being given first choice but rather from the major lack of housing in this country.
"The idea of a native-born preference for social housing is clearly discriminatory ... Social housing should be allocated on the basis of need and nothing else.
"This is supposed to be a Labour government, so why are some ministers allowing the BNP to dictate our policies?"
Mr Livingstone added: "Margaret Hodge's suggestion that housing allocation should be based not on need but factors like length of residence would be catastrophic for community relations ...
"Politicians in general, and government ministers in particular, should get their facts right before making statements with the potential to do great harm to the good community relations on which the prosperity of all Londoners depends."
The Refugee Council pointed out that asylum seekers are not entitled to council housing, and that immigrants from new European Union countries face restricted access to benefits.
Yesterday, Jon Cruddas, the Labour deputy leadership hopeful and MP for Dagenham - which borders Mrs Hodge's Barking constituency - said that the minister's comments were "not only wrong; they are also inflammatory".
An early day motion tabled by Ms Abbott and supported by Keith Vaz, the former Europe minister, expresses regret at "the honourable member for Barking's recent call to give British people housing priority over immigrants".
It adds that the MPs do "not believe that the current housing crisis will be solved by scapegoating homeless families on the basis of race, ethnicity or national origin".
Mr Vaz said: "It is important to challenge false assumptions as soon as they are made. Margaret appears to want to be the Alf Garnett of Islington."