Lord Mandelson says he likes to inject some humour into the workplace
Lord Mandelson has warned that Gordon Brown could face a further challenge to his leadership in the future.
The business secretary told the Daily Telegraph that opposition to Mr Brown could re-emerge, and some Labour MPs would not be "reconciled" to him as PM.
Meanwhile, Foreign Secretary David Miliband has admitted he considered resigning at the same time as his former cabinet colleague James Purnell.
He told the Guardian he discussed his decision with Lord Mandelson.
The business secretary, who was last week given the additional title of first secretary of state, said he would not "lose any sleep" over the threat posed by those Labour MPs who opposed Mr Brown's leadership of the party.
He told the paper: "There's a small group who keep coming back... they wouldn't have voted for him in the first place."
In the interview he acknowledged that a string of ministerial resignations, including that of the former Work and Pensions Secretary James Purnell, caused "a serious ruction".
But he praised Gordon Brown's leadership, saying: "I couldn't work for somebody as I do for Gordon if I didn't believe in them and respect them."
Harriet Harman, Labour's deputy leader, said the party's job was to help combat the country's problems rather than concern itself with "inner turmoil".
She praised Gordon Brown as a man who had helped the government improve schools and hospitals.
Asked about Mr Mandelson's apparent growing influence in the party, she said: "I think we all have an important role to play."
In a separate interview in the Guardian, David Miliband said he discussed his decision about whether to resign with Lord Mandelson.
The foreign secretary said he had made up his mind to stay on the day of the local and European elections.
He said: "I'd made my decision on Thursday... sometimes you can make your decisions with great planning and calculation and sometimes you have to make them rather more quickly."
And although he reached a different conclusion, Mr Miliband said he respected the decision the former work and pensions secretary, Mr Purnell, had taken.
"James made his decision in good faith; I made my decision in good faith," Mr Miliband told the paper.
'Fight of its life'
In the interview, Mr Miliband admitted that the question of the party's leadership arouses passionate feelings.
"This divides people who are close and people feel passionately one way and people feel passionately the other way."
But the foreign secretary said it was important now that the Labour party sets out what it, and Gordon Brown, stands for.
He admitted the task in front of the party is huge following the local and European election results and said it had "the fight of [its] life on [its] hands."
But he added: "The government is much stronger for Peter at the heart of it."
Lord Mandelson is widely credited with helping Mr Brown see off the challenge to his leadership.
In his interview, the business secretary suggested three priorities for Mr Brown going forward: a greater focus on the economy, public service reforms, and delivering "people power" over services such as health and education.
He also spoke about his own ideas of what makes a good leader.
He said: "I believe in leadership and in being decisive. Secondly, in listening to people and respecting official advice you receive. And thirdly, introducing a bit of humour and jollity to your work.
''You don't have to be too grey or serious the whole time. You can do your work and enjoy it at the same time and include people along the way."