Labour will accept some of the Chancellor's radical welfare cuts, Harriet Harman said in an intervention which has exposed divisions within the party over how to respond to George Osborne's plans.
Acting Labour leader Ms Harman said her party had to acknowledge that it lost the election because voters did not trust it "on the economy and on benefits".
She said the party would accept the overall household benefits cap and Mr Osborne's decision to limit support through tax credits and universal credits to two children.
But her comments opened up a rift with the contenders to replace Ed Miliband as the next permanent leader of the party.
A spokesman for Labour leadership contender Andy Burnham said he opposed the cuts to child tax credits.
"George Osborne did not set out the details of these cuts before the election and he has no mandate for them. David Cameron even denied they would happen," the spokesman said.
"We have seen time and time again with this Tory government that the devil is in the detail, and we're still waiting for George Osborne to set out the details on his cuts to tax credits.
"As we have previously said, Andy opposes cuts to child tax credits. These are paid to people who are doing the right thing and working hard to make ends meet.
"Andy will not offer blanket opposition and, where we agree with a Government policy, we won't oppose for the sake of it. But these tax credit changes are regressive, they are wrong, they hit families in work and Andy opposes them."
A spokeswoman for Yvette Cooper said: "Yvette has made clear from the start that she does not believe the best way to reduce the deficit is to hit working families, reduce work incentives and push more children in to poverty.
"She has said that the Tory plans for cutting tax credits and abandoning the child poverty target do both and Labour should strongly oppose them.
"She believes Britain needs an alternative approach - and that Labour should argue for a real alternative to Tory plans."
Jeremy Corbyn, the most left-wing of the leadership candidates, said: "If it is proposed that Labour MPs are being asked to vote for the Government's plans to cut benefits to families I am not willing to vote for policies that will push more children in to poverty.
"Families are suffering enough. We shouldn't play the Government's political games when the welfare of children is at stake."
The Labour position outlined by Ms Harman is an attempt to regain the trust of voters on the crucial issue of financial responsibility.
She told BBC1's Sunday Politics: "I think we won't oppose the Welfare Bill. We won't oppose the household benefit cap. I mean, for example, what they brought forward in relation to restricting benefits and tax credits for people ... with three or more children.
"I mean, what we've got to do is listen to what people around the country said to us and recognise that we didn't get elected, again, and this wasn't a blip, this was the second time we haven't got elected, and actually what people don't want us to do is they don't want us to do blanket opposition, they want us to actually be specific about what we are going to be challenging and holding the Government to account on, but more than that, they want us to listen to their concerns and we've got to recognise why it was that the Tories are in government and not us.
"Which is not because people love the Tories particularly, but because they didn't trust us on the economy and on benefits."
Explaining her stance on the future child tax credit limit set out in the Budget, she said that during the election campaign she talked to parents who would say they would love to have another child, "but we just can't afford it".
"They're working hard and they feel that it's unfair on other people, that they can have bigger families that they would love to have if they were in the position to do that. Now we have to listen to that."
Ms Harman said Labour would oppose some of the changes to tax credits, which would hit low-paid workers despite the announcement of the new national living wage (NLW).
"Obviously we welcome the increase in what they're now calling the National Living Wage, but pointing out that there will be three million families who are working hard who are actually going to be £1,000 worse off. So we will oppose that.
"We will oppose too the abolition of the child poverty targets, but actually we're not going to do blanket opposition because we've heard all around the country that whilst people have got concerns, particularly about the standard of living for low-income families in work, they don't want blanket opposition to what the Government are proposing on welfare."
Her comments came as Business Secretary Sajid Javid rejected the assessment of the independent Institute for Fiscal Studies (IFS) that the Budget was regressive because it hit the poorest households more than wealthier ones.
Mr Javid accepted that in "any budget there will be some losers, there'll be some winners" but insisted it was a "fair, well balanced" package
The IFS found that the average low-paid worker on tax credits would "unequivocally" lose more from benefit cuts announced by the Chancellor than they would gain from the introduction of the NLW, which will be worth £7.20 an hour to workers aged 25 or more - rising to £9 by 2020 - compared with £6.50 on the current national minimum wage.
Mr Javid dismissed the assessment - but appeared to blunder over the value of the flagship NLW, claiming it would be £7.50 an hour.
He told BBC1's Andrew Marr Show: "This is not a regressive budget. This is a budget when, taken together, it will ensure that the richest make the biggest contribution to the consolidation."