The emails were sent before Lord Mandelson joined the Cabinet
Lord Mandelson has said an e-mail in which he described Gordon Brown as "self-conscious" and "angry" was not intended to be hostile.
The business secretary said the e-mail, written in January 2008 - months before he returned to cabinet - had been "misrepresented" by the Mail on Sunday.
He told the BBC it had simply said the PM had to "be what he is" and not have some "artificial persona" glued to him.
At the same time, Lord Mandelson warned rebel Labour MPs to back Mr Brown.
Asked repeatedly about the e-mail on BBC One's Andrew Marr Show, he said: "I'm not going to comment on every stray Chinese whisper, rumour or old e-mail that other people want to make a mountain out of a molehill of."
Not a pop star
He said the content and context had been "completely misrepresented".
"It was not hostile to or about the prime minister," he said.
"What it said is that the prime minister needs to be what he is, be what he stands for and believes in and the values he has - and not listen to people who are trying to glue some artificial persona onto him."
He added: "The prime minister is a politician, not a pop star. He concentrates on getting his policies right, not being a showman.
I think Gordon Brown has now achieved the impossible he has made the cabinet even more dysfunctional and divided than it was before
William Hague Shadow foreign secretary
The Mail on Sunday and Sunday Times published extracts from the e-mail, sent to former Labour spin doctor Derek Draper.
The Sunday Times said they were part of a wider e-mail debate about a book called the Political Brain, by US psychology professor Drew Western, which looked at which qualities made politicians successful.
The paper reported that Lord Mandelson had written that Mr Brown was "not as comfortable in his own skin" as his predecessor, Tony Blair.
He wrote that Mr Brown should "be himself", adding: "This is not a substitute for policy formulation and taking well-prepared, well-ordered decisions."
'Not so angry'
He said Mr Brown was "a self-conscious person, physically and emotionally" but said it would improve when he won public approval: "Then he will visibly relax. He will be enjoying himself. Not so angry."
It comes at the end of a bitter week for the prime minister, in which Labour was heavily defeated in local elections, six cabinet ministers left the government and his leadership has come under attack.
Ed and I talked on the phone yesterday and laughed out loud about this stupid fabrication
James Purnell's surprise resignation as work and pensions secretary on Thursday came with a call for Mr Brown to "stand aside to give our party a fighting chance of winning". Caroline Flint quit as Europe minister complaining she had been used as "window dressing".
But shadow foreign secretary William Hague told the BBC it appeared the reshuffle had left the cabinet "even more dysfunctional and divided than it was before".
Lord Mandelson dismissed newspaper stories that he had clashed with Ed Balls, the schools secretary who had been widely expected to become chancellor in the reshuffle - in the end Alistair Darling remained in the job.
It had been reported that Mr Balls blamed Lord Mandelson for blocking his move to the chancellorship.
But the business secretary said: "Ed and I talked on the phone yesterday and laughed out loud about this stupid fabrication. It is complete artifice and it is mischievous artifice."
He also said it was not true to suggest Hazel Blears, who quit as communities secretary on the eve of the local elections, did not like Gordon Brown's style of leadership.
"On the day she resigned, she rang me, told me why she was leaving the government. She did not criticise the prime minister and she did not express those sentiments, in her letter or in public or since."
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