Labour leadership contender Liz Kendall has said the policy of removing tax credits to migrant workers is "definitely something we should look at" but called for a wider debate on Britain's future in the EU.
She accused the Prime Minister of putting "internal political management" ahead of the country's national interest.
Ms Kendall told BBC 1's The Andrew Marr Show: "We do have to deal with the issue of people who come here to work. They must be working and not claiming benefits. But this is about something much bigger - it is about the future of our country and our place in the world.
"David Cameron should be focusing on what is in Britain's national interest and our place in the world, not on internal party politics."
Asked if she was in favour of removing tax credits to migrant workers, she replied: "That's definitely something we should look at, but this is a far bigger debate.
"Of course David Cameron is reducing the question because he has failed to show leadership with his own backbenchers.
"He has allowed this to define whether or not Britain remains part of Europe. That is a profound lack of leadership on his behalf because he is more concerned about internal political management than the future of the country."
Pushed on the migration question again, she added: " I'm in favour of free movement of labour but not free movement of benefits. People who come here should come here to work.
"If we allow this debate to be defined by that issue alone, we will be profoundly wrong. This about Britain's place in the world, our future economy."
She reiterated her support for maintaining the 2% defence spending commitment, adding: "Our place in Europe is essential as part of our wider international relationship."
Ms Kendall also failed to confirm whether or not she supports the £3 billion of cuts announced by the Chancellor this week.
Asked about the need to cut the deficit, she said: "Let's see what the Conservatives come out with in their budget. I'm not going to provide a budget response to a budget that has not been delivered
"But it is vital that fiscal credibility is at the heart of all we do because people need to trust us with our money to win but also because there is nothing progressive about spending more on debt interest repayments than spending on the future of educating our children."
Asked again whether the deficit needs to be dealt with, she replied: "The deficit needs to be dealt with, but we need to do far more....this is the really important challenge for the future. How do we get jobs and growth in every part of the country?"
Asked if she supports cuts as a means of getting the deficit down, she said: "We need to balance the books and live within our means but in a better, fairer way.
"When we have seen what George Osborne is proposing I will come back to you.
"Let's see what the details are. We have yet to see many of the commitments that the Conservatives made during the campaign.
"Fiscal credibility and responsibility and living within our means is essential but so too is making sure we have real growth in all parts of the country. Ed Miliband was actually right about that as a big challenge."
Asked if she had enough "heft" to be Labour leader, Ms Kendall replied: "Yes, I do.
"The question for this leadership election is not what jobs people have had in the past but who will face up to what we need to do to win in 2020 to change our country."
Shadow leader of the Commons Angela Eagle, who is running for the post of deputy leader of the Labour party, said her parliamentary career and character were better suited to the second-in-command job.
On Labour's defeat, she told Sky News' Murnaghan the party did not communicate a lot of its policies well enough or effectively bust the "myth" its spending on schools and hospitals caused the financial crisis.
She also accepted Ed Miliband had a problem - as the polls ahead of the election showed - being seen as a prime minister.
But she added: "I think this is a failure of the whole party. We have to take collective responsibility for it rather than blaming individuals.
"I don't think it helps to be uncomradely to people in the party."
Former defence secretary Lord Hutton backed Ms Kendall for the leadership, describing her as "brave and courageous".
The Labour peer told Sky News' Murnaghan: "I think she's going to take the party in the right direction.
"This is a moment in Labour's growth and development that we need to skip a generation.
"I think we have got to put behind us all of the antagonism and disagreements of the past and choose a leader who is unencumbered with any of that and can take the party in the right direction."
Asked what that involved, he replied: "It has got to be on getting Labour back onto the centre ground."
He also said the party needed to lose its "obsession" with putting people's taxes up, become more pro-business and look at its relationship with the trade unions, which could no longer be the "centre of gravity".
Asked if it was new New Labour, he said that was the ground the party could win from rather than continuing to "throw itself at a brick wall".
On what went wrong for Labour, he said: "I think pretty much everything went wrong for Labour. We found ourselves on the wrong side of the main arguments and concerns of the voters. I don't think we struck a chord with our anti-business rhetoric.
"We allowed our opponents to portray us as an anti-business party. There's no appetite any longer in British politics for an anti-business party.
"We have got to think long and hard about the party we should be. I hope we can find a way of coming back onto the centre ground.
"The voters have very rudely told us - 'you weren't on the centre ground'. We have to reflect on that and we have got to reach out, we have got to target Conservative voters again in the way that we successfully did 15 years ago.
"We lost the election to the Conservatives - we didn't lose it to the SNP or Ukip or anyone else."
Labour MP Tom Watson, who is running against Ms Eagle for the deputy leadership, has said there needs to be a woman in the party's top two.
He told BBC Radio 5 live's Pienaar's Politics he would challenge the party to change the rules to make sure a woman gets at least one of the posts if - come September - two men are chosen.
Asked if having two men in charge would be a bad thing, he replied: " For the first time ever there is a genuine choice of very strong candidates who are women in this election.
"We could end up with two women. But I do think it's an issue that needs addressing if arithmetically we end up with two men - a leader and deputy - and I've said that I'll go back to our national executive committee if that's the case to ask them to put them right.
"It's not for me to change the rules but there are ways you could do it. You could either sort of balance .... You could change the rules so that in future you end up with at least one women in the leader or deputy role or you could even split the deputy role."