Yvette Cooper and Liz Kendall have denied reports that Lord Mandelson tried to persuade the three mainstream Labour leadership candidates to quit the leadership contest and force the party to stop the election.
The move by the former politician and 1997 election campaign leader highlights maneuvers within the party to stop Mr Corbyn winning the election.
Ms Cooper said she had not been approached directly by the Labour peer, she was unaware if her campaign team had been contacted.
I’ve not discussed this with Peter Mandelson.
I gather there was some view that maybe the whole process should be stopped because so many people were joining at the last minute. I don’t think that’s right.
I think it’s a good thing that people are joining the party.
Ms Kendall insisted that neither she nor her office had spoken to him.
Former PM avoided naming any Labour leadership candidates in his speech, but appeared to make a veiled warning against electing Corbyn.Read the full story ›
Yvette Cooper has said her Labour leadership rival Jeremy Corbyn - who leads the polls - offers the "wrong answers for the future".Read the full story ›
Yvette Cooper, one of Labour's leadership candidates, said that the government's plans for trade unions are an "ideologically driven attack on Britain's trade unions" which "puts narrow Tory party interests ahead of what is right for the country".
"It not only undermines years of progress on workers' rights, but it also breaks the growing consensus on the need to reform funding of political parties.
"This is another example of the Tories employing cheap divide-and-rule tactics."
Speaking ahead of her nomination for the race to become Labour leader, Yvette Cooper made her case in a speech in central London.
She said the leadership contest "needs to be about the future of the country not just the past of our party if we are to win again".
"We have a long, hard road to support Scottish Labour rebuilding trust in Scotland. A task to win back the trust of Labour voters who switched to Ukip, angry with us and at the world."
She added: "We won't deliver a Labour government by swallowing the Tory manifesto, Tory plans or Tory myths. In the end the Tories don't have the right values or the right answers for our country.
Labour leadership candidate Yvette Cooper has accused her party colleagues of "swallowing the Tory manifesto" since the party's general election defeat.
"I will set out ideas for the future that don't just involve swallowing the Tory manifesto and set out a Labour vision for the future," she told BBC1's The Andrew Marr Show
The comments were quickly perceived as an attack on her leadership rival Liz Kendall but when asked if she was referring to the shadow care minister, Ms Cooper said she did not want to attack specific individuals.
The shadow home secretary also appeared to criticise another leadership candidate Andy Burnham, who said that Labour had appeared "soft" on benefits claimants.
Ms Cooper said it was wrong to "stigmatise" people who were out of work, adding that it was against Labour values.
Labour leadership candidate Yvette Cooper wants to adopt Scandinavian-style system of universal childcare, with 30 hours of free care for all preschool children over the age of two.
Writing in The Independent, Ms Cooper said she wanted to see new tax credits to help parents out in the period after maternity leave finishes, and that the pledge would be a cornerstone of her leadership campaign.
She said: "We should campaign for universal childcare - as other countries, including Scandinavia, have.
"That means breakfast clubs, after-school clubs, holiday clubs and free nursery places and childcare available full-time, not just for three and four-year-olds but two-year-olds too."
Labour leadership hopeful Yvette Cooper has said she will put measures to help families at the heart of her campaign to rebuild Labour after its election defeat.
The shadow home secretary said Labour had to "reach outwards" and "rebuild", winning back voters who deserted the party in favour of the Tories, Ukip and the SNP.
Ms Cooper believes she can smash the "glass ceiling" and become Labour's first permanent female leader, vowing to "shake up the system".
In an interview with The Sun on Sunday (£), mother-of-three Ms Cooper, whose husband and former shadow chancellor Ed Balls lost his Westminster seat in the general election, said Labour had to offer hope to families.
We need to put families at the heart of our politics. As a mum, I feel very strongly about that because my family, my kids are the most important thing in my life.
That has to be reflected in what we do. We have got to reach out and rebuild and that means winning back voters.
We've got to show practical things we can do to help families get on, to know their kids can get an apprenticeship, have a good start in life and go to university.
Yvette Cooper, the shadow home secretary and Labour leadership contender, has accused David Cameron of "taking people for fools" after new figures showed a significant increase in net migration to the UK.
Ms Cooper said there was a "massive gap" between the government's "rhetoric" on immigration and the "reality".
She said: “David Cameron is taking people for fools. On the day he has promised yet again to cut net migration to the tens of thousands, these figures show it is over three times that target.
"This massive gap between rhetoric and reality, between promise and delivery, just destroys trust in anything Ministers say on immigration."
Yvette Cooper has dodged questions about her potential leadership ambitions after a disappointing night for the Labour Party.
When asked by ITV News whether she would be standing for leader if Ed Miliband resigned, she said: "I really don't think we should be talking about this. We have just had an election and we've got a lot more election results to come.
When second journalist repeated the question, Ms Cooper said: "Seriously no there isn't one."