George Osborne and Iain Duncan Smith have insisted they will push ahead with plans to slash another £12 billion a year from the benefits bill.
The Chancellor and Work and Pensions Secretary reiterated their determination to achieve the savings in full after a major anti-austerity protest on the streets of London.
The two men are believed to have thrashed out details of the cuts pledged in the Tory manifesto over the last few days - putting paid to rumours that they could be scaled back or delayed.
They have already said the household benefits cap will be reduced from £26,000 to £23,000 a year and housing benefit and tax credits are expected to bear the brunt.
However, David Cameron has pledged full protection for child benefit and pensioner benefits.
Writing in the Sunday Times, Mr Osborne and Mr Duncan Smith insisted they had inherited a "crackers" welfare system from Labour in 2010.
Repeating the claim that Britain makes up 7% of all the welfare spending globally despite having just 4% of GDP, the pair said the arrangements had "incentivised people to live a life on benefits".
They argued that the new universal credit would rationalise the "Byzantine" network of means-tested payments and ensure it is always in the interests of those on benefits to work more.
The coalition shaved £21 billion off the welfare budget, but Mr Osborne and Mr Duncan Smith warned that it will still make up 12.7% of spending in 2019-20.
"It took many years for welfare spending to spiral so far out of control, and it's a project of a decade or more to return the system to sanity," they wrote.
"This government was elected with a mandate to implement further savings from the £220 billion welfare budget.
"For a start, we will reduce the benefit cap, and have made clear that we believe we need to make significant savings from other working-age benefits.
"We will set out in detail all the steps we will take to bring about savings totalling £12 billion a year in next month's Budget and at the spending review in the autumn.
"As before, all our reforms will have these central aims: to ensure the welfare system promotes work and personal responsibility, while putting expenditure on a sustainable footing.
"Welfare reform is fundamentally about opportunity and changing lives, supporting families to move from dependence to independence - a vital point, because without social mobility there can be no social justice. It is the right thing to do."
Tens of thousands of protesters took to the streets of London, lighting fires and throwing smoke bombs as they demanded an end to the government's austerity programme.
The crowd was addressed by left-wing comedian Russell Brand and singer Charlotte Church among others.
Labour leadership frontrunner Andy Burnham made clear he would oppose cuts to tax credits for people on low incomes, and reductions in benefits for the disabled.
He also insisted the Government's mandate for pushing through £12 billion of welfare cuts was "questionable".
"I have not said there should be no cuts. We do have to bring the deficit down. There has to be a credible plan," he told Sky News' Murnaghan programme.
"It is just I would not do it the way this Government is doing it. They are doing it all from public spending cuts.
"That is going to have some devastating consequences for individuals, who will be very much harmed by that but also for our public services.
"The country is not going to feel good, is it, if we get the deficit down but basically destroy our public services.
"I think this is pretty disgraceful what is going on today. Here we have a Chancellor that is frightening people, basically. He is just waving around this idea of huge cuts, of drastic cuts without saying where they are going to come from.
"If this Chancellor thinks it is acceptable to take benefits off disabled people who cannot replace them, if he is coming after the tax credits of people on low incomes in work then he is going to have a fight on his hands because I will stand up for those people.
"It is questionable whether he has a mandate for cuts on this scale because he didn't spell out before the election where these cuts were going to fall."
Mr Burnham added: "I have said that I will not set my face against reductions in the benefits bill - of course not. Who could in the circumstances that we are in?
"But that does not mean swallowing what the Tories are saying and going along with a brutal plan that is going to hurt many vulnerable people.
"What about the idea of tax incentives for companies paying the living wage? What about the dysfunctional housing market that we have that leads to so much housing benefit being given to private landlords?"
Labour former leadership contender Diane Abbott said she would like to see her party colleague Jeremy Corbyn, who spoke at yesterday's demonstration against austerity, become prime minister.
The MP for Hackney North and Stoke Newington told BBC1's the Sunday Politics: "If the 2010 election had been done on a one person, one vote ballot I would have come third. I think you will be surprised how well Jeremy is going to do.
"He's done two or three hustings so far and he's the one that gets all the applause. On Newsnight the other night, in front of a non-Labour audience, he got the most applause.
"You are going to get a shock. What Jeremy is saying is actually very popular."
Asked if she wanted to see Mr Corbyn as prime minister, she said: "I would like to see Jeremy Corbyn or somebody with Jeremy Corbyn's politics definitely leading this country.
"I think what people want is politicians who are authentic, politicians who believe in something and politicians who are prepared to put themselves on the side of the 99% rather than 1% and Jeremy is the leader who will put himself on the side of the people."
Labour MP Frank Field, newly-elected chairman of the Commons Work and Pensions Committee, questioned whether the proposed cuts were "mirror or reality".
"George Osborne and Iain Duncan Smith's enthusiasm to get £12 billion from the welfare budget by getting claimants into work should be shared by all parties," he said. "But both these two architects of this policy seem to have mistaken cutting the true cost of welfare for simply moving claimants from one benefit like jobseeker's allowance to another which is working tax credit. The overall bill isn't cut.
"The real challenge which I hope the Work and Pensions Select Committee will face is not simply of getting more people into work on taxpayer subsidised low pay, but once they're in work to increase their satisfaction and that of taxpayers by ensuring there is a ladder to higher real incomes. That's the only way now to cut the welfare bill fairly and permanently."