Peter Mandelson fields questions over his meetings with Oleg Deripaska
Lord Mandelson has begun a four-day trip to Moscow with the Tories asking him to "get things straight" over his dealings with a Russian billionaire.
The business secretary has said he gave no favours to Oleg Deripaska during his time as European trade commissioner.
But shadow foreign secretary William Hague said the "whole country" wanted "transparency" about previous meetings.
Prime Minister Gordon Brown said Lord Mandelson's dealings with Mr Deripaska had been "found to be above board".
The visit to Moscow is aimed at improving trading relations between Russia and the UK.
Controversy has surrounded events at a summer party on board Mr Deripaska's yacht, attended by Lord Mandelson, when he was still the trade commissioner.
William Hague on Labour and Tory dealings with Oleg Deripaska
Last week, the minister admitted first meeting the aluminium magnate in 2004 - two years earlier than officials had previously said.
Lord Mandelson's relationship with Mr Deripaska has led some to suggest he could have intervened in EU policy on the Russian's behalf.
In 2004, Lord Mandelson proposed that tariffs on aluminium imports be cut from 6% to 3%
Confirmation that he had met Mr Deripaska in 2004 prompted calls from Liberal Democrat MP Norman Baker for the business secretary to release full details of the meetings.
But Lord Mandelson told Sky News: "A lot has been said about the relationship I have with one particular Russian businessman.
"All I would say about that is that he has never asked for any favours, I have never given him any favours and that is what the European Commission in their examination of the issue has very firmly put on record."
'What was discussed?'
The European Commission insisted on Saturday there had been "no political interference" from Lord Mandelson in decisions to ease EU import duties. It said its decisions had been taken in "full transparency".
Mr Brown told BBC One's Politics Show: "It's all been looked at and it's all been found to be above board I really know nothing more about this other than that the European Commission has dealt with it."
But Mr Hague told BBC One's Andrew Marr Show: "We and, I think, the whole country do want to know transparently about the meetings that have happened and what was discussed at them and whether they ever discussed aluminium tariffs and so on.
The political debate will come back to the fundamentals and that's about who actually is best equipped and best able to take the country forward in a very difficult period
"If Peter Mandelson could put the record straight on that then I think the media could move on."
However, Tony Blair's former spokesman Alastair Campbell said: "Peter's return to government, I think, is a good thing for the government.
"I think Gordon needs a few big hitters around and Peter, whatever else he is, is a big hitter.
"And I think this story, it's kind of still running and it's got legs yet.
"Well, fine, eventually it will run out and the political debate will come back to the fundamentals and that's about who actually is best equipped and best able to take the country forward in a very difficult period."
Communities Secretary Hazel Blears told Sky News: "You've heard from Peter directly. He was asked for no favours; he gave no favours.
"The European Commission say it's actually part of the job of a trade commissioner to be out there trying to maximise trade and industry and Peter is going to out right around the world making sure that Britain gets the best deal in terms of investment - and that's what I want Peter Mandelson to do and I know that's what he's focused on."
On the Andrew Marr Show, Mr Hague was also asked about shadow chancellor George Osborne dealings with Mr Deripaska while on holiday on the Greek island of Corfu.
Financier Nathaniel Rothschild has accused Mr Osborne of attempting to solicit a £50,000 donation for the Conservative Party from the Russian businessman.
It is illegal for people not on the electoral roll to give to a UK political party, and Mr Osborne has vehemently denied trying to persuade Mr Deripaska to do so.
Mr Hague said: "I think we all learn from a media storm - and certainly I have in the past - and George Osborne is a very talented colleague and a close friend and we will all learn from this situation."
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