Trade minister Margaret Hodge was echoing the policy of the BNP when she commented on housing allocation, BNP leader Nick Griffin has told the BBC.
The BNP said it agreed with Mrs Hodge's views on housing allocation
Mr Griffin said he agreed with Mrs Hodge when she said British people should be given priority over migrants.
But he added that she should also speak about the impact of immigration on health, education and unemployment.
Mrs Hodge has been criticised for her comments, but she said she was simply reflecting her constituents' concerns.
Mr Griffin told Newsnight: "She has just said what we were saying five years ago.
"I agree with her. Where we differ is that she is only talking about housing.
"She should be talking about the impact of immigration on other things as well such as health, education, unemployment and in fact on the whole identity of this country."
Mrs Hodge's Barking constituency, in East London, has been hit by a severe housing shortage, with the council house waiting list standing at more than 8,000 families.
It has also seen a big increase in the number of migrants in recent years, with the non-white population estimated to have doubled since 2001.
Mr Griffin claimed Mrs Hodge's constituency was being transformed because of immigration "against the wishes of the locals".
He added: "That's what Margaret Hodge is worried about - she wants to hold her seat."
Education Secretary Alan Johnson earlier accused her of "using the language of the BNP" and Jon Cruddas and Peter Hain, who like Mr Johnson are Labour deputy leadership hopefuls, have also attacked Mrs Hodge.
Her critics say she is wrong to suggest immigration is to blame for housing shortages, saying "only 1%" of social housing was occupied by foreign nationals.
Policy change call
The BNP, which is accused by its opponents of stirring racial hatred by blaming housing shortages on immigrants, won 11 of the 13 seats it contested in Barking and Dagenham in 2006 elections, making it the second largest party.
During the 2005 general election campaign, Mrs Hodge said the area's change from a white area to a multi-racial community had caused some Labour voters to be tempted by the BNP's policies.
Speaking last weekend, she called for social housing policy to take account of length of residence, citizenship and national insurance contributions.
"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," she said.
Responding to the storm of criticism her comments provoked, she said she was aware it was a difficult issue, but she was listening to her constituents and wanted to start a debate.
She won some support from Labour chairman and deputy leadership contender Hazel Blears, who agreed there was a need "to tackle these tough issues".