Lord Mandelson is on a four-day trade visit to Russia
Lord Mandelson has refused to offer more details on his links to Russian billionaire Oleg Deripaska.
The business secretary, on a trade visit to Moscow, told the BBC "the British media will have to write their own stories".
He added that his concern was "Britain's own national interest" and "the future of its economy".
Controversy has surrounded the minister's relationship with Mr Deripaska while EU Trade Commissioner.
His relationship with the aluminium magnate has led some to suggest he could have intervened in EU policy on the Russian's behalf.
Questioned during his trip to Russia, Lord Mandelson said: "The British media will have to write their own stories and decide what their interests are.
"What I'm interested in is Britain's national interest, the future of our economy, the growth of our businesses and jobs back at home."
Lord Mandelson was a guest on Mr Deripaska's yacht, off Corfu, during the summer.
Last week, he admitted first meeting the businessman in 2004 - two years earlier than officials had previously said.
In that year, Lord Mandelson proposed that EU tariffs on aluminium imports be cut from 6% to 3%.
But he said on Sunday that Mr Deripaska had "never asked for any favours", adding that he had not "given him any favours".
Lord Mandelson added that this was what "the European Commission in their examination of the issue has very firmly put on record".
On Sunday, the Conservatives urged Lord Mandelson to "get things straight" over his dealings with Mr Deripaska.
However, on Monday the minister told the Guardian newspaper: "What is important is not where you meet somebody or how long you meet them for but what you do during the meeting.
"In my case, I offered no favours and I received no favours, unlike [shadow chancellor] George Osborne, who was holding conversations around his visits in order to obtain a financial contribution to the Conservative party."
Mr Osborne vehemently denies attempting to solicit a £50,000 donation for the Conservative Party from Mr Deripaska, having met him several times while on holiday in Corfu.
He was accused of doing so by financier Nathaniel Rothschild.
In an interview with BBC Radio 4's The World at One, Mr Osborne said: "I neither asked for money nor received any and I didn't break any rules but I think I did make a mistake."
He added: "To be honest this didn't look very good and that's something I regret."
Mr Osborne has said he will no longer carry out fundraising for the Conservatives.