He resigned twice from cabinet posts - once over a loan from his ministerial colleague Geoffrey Robinson and once over allegations of misconduct over a passport application for the Hinduja brothers, for which he was later cleared of any wrongdoing.
Since his appointment there have been stories in some newspapers about his links with Russian billionaire Oleg Deripaska.
The Mail on Sunday reported an Italian tycoon Diego Della Vale, who benefited from EU trade tariffs, had played host to Mr Mandelson several times.
On Thursday the Conservative MP Hugo Swire called for a Commons debate on the "very serious nature of some of these allegations".
But on BBC One's Andrew Marr programme the business secretary dismissed the claims as "muck-raking stories that have appeared in some of the Conservative newspapers".
"I have a very clear view of my public role and the responsibilities I have in that public role and how I spend my private time," he said.
"There has been innuendo in the newspapers that I gave favours or I gave benefits as trade commissioner to certain individuals because of my personal friendship with them.
"The entirety of the European Commission, the director general for trade himself, has made clear there is not one jot of truth in that, that it is 100% false."
He added later: "You cannot do business as a European trade commissioner in Russia, India, China, South Africa, Brazil, all the big emerging economies of the world, without having contact with the big business and economic figures in those countries as well as the political figures."
Lord Mandelson fell out with Mr Brown in the 1990s when he decided to back Tony Blair for the Labour leadership.
Asked about his relationship with Mr Brown, he said it had had its "rocky moments".
He said: "I think both of us looking back would say we wasted a lot of the energy and time that we could otherwise have devoted to the success of the government by not repairing our relationship sooner."
However, he said the rift had been repaired and it was time to "leave the past behind us".
Lord Mandelson said voters were now looking at Mr Brown "afresh" because of the way he had handled the financial crisis, and were saying he was decisive and capable of bold measures.
"He's not a showy person, he's not an attention-seeking person, he's not swinging around like a pendulum in the way that [Conservative leader] David Cameron is," he added.
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