Senior Conservative cabinet minister Iain Duncan Smith has said limiting child benefit to the first two children in a family is well worth considering and could save a significant amount of money.

The work and pensions secretary hinted the move was being examined by his party despite previously being vetoed by Downing Street over fears it could alienate parents.

Asked about the idea on the BBC’s Sunday Politics programme, Duncan Smith said it could also “help behavioural change” in what appeared to be a suggestion that it could discourage people struggling with their finances from having more children.

“I think it’s well worth looking at,” he said. “It’s something if we decide to do it we’ll announce out. But it does save significant money and also it helps behavioural change.”

The idea was initially proposed late last year by Nadhim Zahawi, a Conservative MP and member of the Downing Street policy board, but it was quickly squashed by No 10.

George Osborne, the chancellor, has indicated the Conservatives will need to find annual savings of about £12bn from the welfare bill during the next parliament, without yet specifying how all of this sum would be cut from the budget.

Some of the savings are expected to come from targeting housing benefit for under-25s and by means-testing people on incomes of £60,000 to £70,000 who live in social housing.

At the party’s autumn conference, Osborne said about £3bn would be saved by a two-year freeze on benefits and tax credits. However, he has all but ruled out cutting universal benefits for pensioners, suggesting the bulk of the rest of the savings will have to come from working-age people.

Earlier this year, the Policy Exchange thinktank revived the proposal for child benefit cuts, suggesting it should be limited to four children per household. Researchers argued that this could be justified because the arrival of a first child tended to have the biggest impact on family finances, and said the move could save about £1bn over the course of a parliament.

The thinktank said the child benefit rates should continue to rise at a rate of 1% for the first and third child of a household and by 2% for the second child for the rest of the next parliament. The weekly payment for a fourth child should remain at next year’s level and payment should be scrapped altogether for fifth and subsequent children born after April 2016.

Many proposals by Policy Exchange, founded by a group including ministers Michael Gove, Francis Maude and Nick Boles, have found their way into Conservative manifestos in the past.

Its report said a poll it commissioned from YouGov found more than two-thirds of people would support capping child benefit at four children. It said there was widespread support for a cap among Conservative voters – at 83% – while the majority of Labour voters (56%) and Liberal Democrat voters (63%) were also in favour.

The policy is already supported by Ukip, whose website says “child benefit is only to be paid to children permanently resident in the UK and future child benefit to be limited to the first two children only”.