Mr Duncan Smith said a "very, very significant number" of people had gone out to work in affected households within the four London boroughs where the cap has already been implemented.
"A very, very significant number have gone out to work; in fact, what the jobcentre staff have told us as we have been going round is that they have seen a genuine increase since they have alerted people to the fact that they are likely to be in the cap," he told BBC Breakfast.
He added: "This is both about saving money and, more particularly, about changing a culture that had left families, particularly large families, finding it easy and a reality for their lives to stay out of work on taxpayers' benefits."
Mr Duncan Smith said the "greatest effect" of the benefits cap would be in London and the South East. "The key principle behind this all over the country is that those who work, those who are trying to do the best in their households, do not see others who are down the road, who are on benefits, on welfare, actually getting more than they do," he said.
Mr Duncan Smith rejected suggestions that jobs were not available for claimants who wanted to go back to work. "The private sector has been providing jobs. Every week something like half a million new jobs are in the jobcentres and out in the universal job match that we have now produced," he told the BBC Radio 4 Today programme.
Matthew Reed, chief executive of the Children's Society, accused the Government of trying to use a "blunt instrument" to solve a complex problem.
"The debate around this cap has focused solely on workless adults, but the reality is that children are seven times more likely than adults to lose out," he said. "140,000 children, compared to 60,000 adults, will pay the price as parents have less to spend on food, clothing and rent.
"And almost half the adults affected will have children aged four or younger, and would find it extremely difficult to be in work, even if they could afford childcare which can cost as much as £100 per child per week."