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Rudd quit late on Sunday after she said she had inadvertently misled parliament over the controversy.
The government has faced criticism over its treatment of some long-term Caribbean residents who were wrongly labelled illegal immigrants.
"The most urgent task I have is to help those British citizens, that came from the Caribbean, the so-called Windrush generation, and make sure that they are all treated with the decency and the fairness that they deserve," Javid told broadcasters.