Yvette Cooper has ruled out any deal with the SNP after the next general election if she become Labour leader.
The shadow home secretary said that she could not foresee an arrangement with a party that wants Scotland to leave the UK.
She also predicted that David Cameron would reprise fears over the SNP to win votes in England in 2020.
Former Labour leader Ed Miliband ruled out a deal with the SNP just before his party's disastrous loss in May.
But some within his party criticised him for not making the decision earlier.
The Tories ran campaign attack ads in England suggesting that the SNP would determine Labour policy in the event of an alliance between the two.
The adverts included one which showed Alex Salmond with Mr Miliband in his pocket.
Ms Cooper said that she was "worried about the careless way in which David Cameron thinks it is ok to play on the fear of Scotland, as the way for (the Tories) to get more votes.
"I think that they will continue to do this and it's a real challenge for the Labour Party.
"For us to try and build that sense of things that we have in common rather than things that pull us apart."
She said the issue was one of the reasons she felt the UK should reconsider having a written constitution.
At the moment, she said, "you can see our written constitution now being stretched to the seams and we need to talk about the values we share".
On a deal with the SNP she added: I don't think you can have any kind of agreement with a party that wants to separate a country or fracture a country in that way."
She also described the days of political wives greeting their husbands onstage after their annual party conference speech as outdated.
But Mr Miliband's wife and David Cameron's wife Samantha performed similar roles last year.
Ms Cooper said that she ruled out ever following suit when her husband Ed Balls stood for the Labour leadership in 2010.
She added: "I think we should be long beyond the era of expecting any politician to have the political wives standing next to them...
"I think that role in terms of the party conference is an outdated one."
Meanwhile, another leadership candidate Liz Kendall rejected the idea of a separate Scottish Labour party after meeting with MSPs.
She said she had come to Scotland because "we had a catastrophic defeat and we need to make big changes".
"If I'm next the Labour leader it will be a top priority for me to be working with our Scottish MSPs, our Labour councillors, they are our frontline in the fight back to win in Scotland and to win in the UK," she added.
"I'm not a centraliser, I believe in devolving power and control. There needs to be greater autonomy, but I don't believe in an independent Labour party just as I don't believe in an independent Scotland.
"We're Labour because we believe in solidarity. We achieve more through our common endeavour than we do alone."
She added that she had no favourite among Scottish leadership contenders MSPs Kezia Dugdale and Ken Macintosh.
Ms Kendall and Ms Cooper are running against fellow MPs Andy Burnham and Jeremy Corbyn.
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