In "The Third Man", which has gone on sale in the UK, Mandelson recounts his years as a key figure within successive Labour governments and his experience of the feud between Tony Blair and the man who succeeded him as prime minister, Gordon Brown.
Mandelson's often gossipy details of the two men's difficult relationship have provoked anger from former colleagues.
"I think you have to write these things when they are fresh in your mind and when they are relevant to a debate that's taking place," Mandelson told BBC radio.
With a four-month-long leadership contest to succeed Brown under way, the flamboyant former EU trade commissioner said he wanted to "give my views and analysis at a time when it is most relevant to the party".
But leadership contender Ed Miliband this week responded to the controversy of the book's imminent launch by calling on the party to start focusing on issues, and not personalities during the election campaign.
"We do need to move on from some of the psychodramas of the past, some of the factionalism that there was," Miliband told BBC radio on Tuesday.
In extracts of the book published by The Times newspaper, Mandelson -- nicknamed "The Prince of Darkness" by opponents for his behind-the-scenes influence -- claimed Blair once called Brown "mad, bad and dangerous".
Other extracts described how Brown's hopes of clinging to power after the election in May by forming a coalition with the centrist Liberal Democrats were scuppered by LibDem leader Nick Clegg, who said he could not work with him.
But Mandelson denied the book showed the former prime ministers and other Labour figures in a bad light.
"I do think it shows a very good and flattering picture of not just Gordon Brown and Tony Blair but others like me who helped them rescue the Labour party from what it was in the 1980s," he said.
In the latest excerpt from the book, Mandelson reveals he tried to push first Tony Blair and then his successor as prime minister, Gordon Brown, to be the first president of Europe.
Mandelson, who at the time was trade minister, promoted Blair's suitability for the job last year when the former premier's name was mentioned among potential candidates.
But when it became clear that Blair would fail to gain the support of enough European Union states, Mandelson turned his attention to Brown.
Mandelson admitted he had a double agenda, believing it would help Labour's bid for re-election if the unpopular Brown took up the new job in Brussels allowing the party to enter last May's general election with a new leader.
Brown is said to have told Mandelson: "If I stood, they would have me."
Mandelson wrote: "If it was true, it struck me that it would be good for Gordon, good for Britain and very possibly good for our electoral chances. 'Are you interested?' I asked him. 'It's a good job.'
"He quickly replied, 'No. No.' I let it drop."
European Union states eventually opted for the low-key Belgian prime minister Herman Van Rompuy as president, and Labour under Brown were voted out in the general election after 13 years in power.
