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It is the second time Mr Mandelson has been forced to leave the cabinet in disgrace since Labour came to power in 1997.
Mr Mandelson, a close confidant and friend of the Prime Minister, Tony Blair, said he did not accept he had acted "improperly in any way" over the passport affair.
Earlier, Mr Blair had summoned him to Downing Street to "establish the facts" of his involvement.
Mr Mandelson has come under increasing pressure over the issue since the weekend.
He has strongly denied claims he pulled strings to help Srichand Hinduja secure a UK passport in return for a £1 million sponsorship deal for the Millennium Dome while Mr Mandelson was in charge of that project.
The Hinduja family is one of the most influential in the world and runs the transnational Hinduja group, a company with assets amounting to around $8 billion.
Since 1990 Srichand Hinduja and his brothers Gopichand and Prakash have been defending themselves against criminal allegations in a long-running corruption case involving an arms deal between Swiss company Bofors and the Indian government.
Srichand Hinduja, who with his brother Gopichand has lived in London since 1979, had his first application for UK citizenship refused in 1990.
Just after paying the sponsorship money, he asked Mr Mandelson whether he could apply again.
The passport was granted soon afterwards.
This week has seen a damaging about-turn by Mr Mandelson's office over a telephone call to the Home Office about Mr Hinduja's case.
On Monday Downing Street said Mr Mandelson's private secretary made the call.
But on Tuesday the prime minister's spokesman admitted Mr Mandelson himself had phoned to discuss the application.
Mr Mandelson insisted there was "no wink or nudge" involved in what he called an "innocent inquiry" made on Mr Hinduja's behalf.
His resignation has sent shockwaves around Westminster, coming as it does only months before the next general election.
Although the passport row was regarded as damaging there were few who believed it would lead to Mr Mandelson being forced out of the cabinet so abruptly and for an unprecedented second time.
Mr Mandelson was first forced to leave the cabinet in 1998 over an undisclosed loan of £373,000 from his then fellow minister Geoffrey Robinson to buy a house in London.
The next day, Minister for Europe Keith Vaz also became embroiled in the affair after it was revealed he had written to both the prime minister and Mr Mandelson about the Hinduja brothers in 1997.
An inquiry, led by Treasury solicitor Sir Anthony Hammond QC, cleared both Mr Mandelson and Mr Vaz of any wrongdoing in March 2001.
However, it concluded it was "likely" Mr Mandelson had made the disputed phone call to Home Office Minister Mike O'Brien - despite the inability of the Home Office to produce records of that day's business.
After new documents came to light concerning the phone call, the inquiry was re-opened a year later, in March 2002. It upheld the conclusions of the first that Mr Mandelson had done nothing wrong.
Peter Mandelson returned to high office with his appointment in August 2004 as EU Trade Commissioner, one of the most powerful jobs in the European Union.
In May 2005 a court in India cleared the Hinduja brothers of any involvement in the Bofors case, citing lack of evidence.
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