Education Secretary Bridget Phillipson has said the government is looking at scrapping the two-child benefit cap but warned it would "cost a lot of money".
Speaking to the BBC, the minister said the policy – which prevents most families from claiming means-tested benefits for any third or additional children born after April 2017 – had pushed people into poverty.
However, she said "seeking to unwind that and to change the social security system is not easy", adding that the price tag would be big.
The government is expected to announce its decision on the cap in autumn, when it publishes its child poverty strategy.
Phillipson, along with Work and Pensions Secretary Liz Kendall, is leading the Child Poverty Taskforce putting together the strategy. It had been due to be published in spring but has now been delayed until the autumn.
The taskforce was launched last year, at a time when the government was being urged by the SNP and some Labour MPs to scrap the cap.
Pressure from Labour backbenchers over the issue – as well as cuts to welfare – have intensified since the Labour's poor performance at the local elections earlier this year.