Iain Duncan Smith has denied reports that ministers are considering trebling "fitness to work" tests on people claiming incapacity benefit.
The work and pensions secretary said the government had "absolutely no intention" of changing the 10,000-a-week rate begun under Labour.
He also played down reports of extra cuts to incapacity benefit.
They were continuing Labour's plan but hoped to get more people working by extending support programmes, he said.
Mr Duncan Smith's comments follow remarks from Chancellor George Osborne, that benefits which the government had not given specific commitments to protect would be part of the summer spending review aimed at cutting the £155bn deficit.
Over 2.5m people are on incapacity benefit or employment support allowance - costing about £12.5bn a year.
The government has said that NHS and foreign aid spending will be protected as it seeks to tackle Britain's budget deficit, but other government departments face 25% real terms cuts.
Mr Osborne has said that figure could be reduced, if more savings can be found in the welfare budget - on top of the £11bn cuts he has already outlined.
He said: "We have got to look at all these things, make sure it protects those in genuine need, protects those with disabilities and protects those who can't work but also encourages those who can work into work. That is the purpose behind our welfare reform."
The Guardian reported that ministers were considering trebling the rate at which "work capability assessments" of people on employment support allowance from the current 10,000-a-week.
But Mr Duncan Smith told MPs said he knew there had been "some speculation in the media" but they intended to launch their "work programme" in 2011, "as we said previously".
"We have absolutely not intention of changing this current plan ... at present 10,000 claimants a week over the period."
He said Labour's own plan had been a "good programme" adding: "We want to make that happen".
Ms Cooper challenged him about where he was intending to find additional savings - Mr Duncan Smith said they intended to roll out Labour's "work support programme" from two areas to across the country. Ms Cooper asked him where the extra jobs would come from.
She argues that the government's plans are simply benefit cuts, not reform, as they would not help people get jobs.
She said the Labour government had already outlined plans to save £1.5bn on sickness benefits through its own test - the work capability assessment.
Earlier she accused the government of a "slash and burn approach" to benefits - including plans to cap housing benefit - which could actually end up costing more in the long run, by increasing unemployment and homelessness."
Equalities minister Lynne Featherstone has also expressed concern at the proposals.
Writing on her blog, the Lib Dem MP said: "The previous Labour government tried to get people off such allowances and my experience as a local MP from surgery is that the 're-assessment' of people claiming has been variable at best."
In the Budget Mr Osborne announced there would be new caps on the amount people could claim in housing benefit, tax credits were reduced, child benefit was frozen and medical tests introduced for the disability living allowance from 2013.
The Conservatives and the Liberal Democrats had already said they would reassess all claimants of incapacity benefit and its successor, the employment and support allowance, for their "readiness to work".
Those deemed fit to get a job would be moved onto Jobseeker's Allowance instead - amounting to a cut in benefits and a requirement to seek work.
Under assessments carried out under Labour on new employment support allowance claimants between October 2008 and August 2009, 39% were deemed "fit for work" and a further 37% withdrew their claim before the test was complete.
Overall, of completed assessments, 68% were deemed fit for work, 9% were recommended for a support group aimed at several disabled people who are not obliged to find work.
The remaining 23% were recommended for a "work related activity group", with which a personal adviser carries out interviews and helps them get ready to return to work.
The Conservatives have argued that one in five incapacity claimants is fit for work - about half a million people. Before the election they suggested that could save £200m a year.
On Sunday, Mr Duncan Smith said he wanted unemployed council tenants to be given incentives to move to areas where there are jobs.
He argued that millions were trapped in "ghettos of poverty" unable to move for fear of losing their homes and people were "trapped" in areas with high unemployment.
He said his plans were about assisting people, not forcing them to uproot.
But Labour MP Louise Ellman, MP for Liverpool Riverside, told BBC Radio 4's Today programme the argument ignored the "need for regional investment in local areas".
"What the government seems to be saying is abandon regional investment and encourage individuals to move out - if you can find the homes they can live in. That isn't a policy, it's going back to the 80s and we don't want that."