There is "no suggestion that Mark Harper knowingly employed an illegal immigrant", Downing Street have said.
The Immigration Minister has announced his resigned over the issue.
Number 10 said David Cameron had "accepted his resignation with regret".
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Addressing an audience in America, the former PM said of Europe's single currency that it was not working "as intended".
The countries lawmakers voted to impeach President Park Geun-hye in the wake of mass protests against her.
The former presidential candidate, who has herself been the target of false news reports, said such stories had 'real-world consequences'.