Prime Minister John Key has signalled his Government will not change its mind and introduce the in-work tax credit for beneficiary families.
The Child Poverty Action Group (CPAG) and other child welfare advocates want beneficiaries to receive the credit, which they say would bolster incomes and help relieve child poverty.
The group said the prime minister's belief that child deprivation was too complex an issue to be solved with a little more cash was not supported by what happened when Working for Families was introduced.
CPAG economics spokesperson Susan St John said it was precisely the extra money provided by Working for Families that improved the lives of thousands of children.
"It was very effective in improving the poverty rates for children in families that were in work, so more money actually does matter."
Ms St John said good housing, child care and access to health care were also important.
Mr Key said today that if child poverty could be ameliorated by just more money, past governments would have already done it.
He said getting people into work and helping them to do that was better than just giving them more cash.
But Ms St John said it was precisely the extra money provided by the Working for Families programme, beginning in 2004, that raised so many children out of poverty.
She said extending the in-work tax credit to beneficiary families would be a very cost-effective way of improving the lives of the country's poorest youngsters.
Mr Key told TV3 programme The Nation that neither his Government nor the Labour opposition favoured introducing an in-work credit to beneficiary families, though work is underway on other solutions to child poverty.
"I think it's worth remembering when Working For Families was essentially established in its new form, because it was established under a National Government, Labour themselves came up with that policy and it was Labour that fought very strongly not to have the in-work tax credit paid to those people," he said.
"So the question is, can we do other things for those families?"
Mr Key said the Government was focused on housing, debt, childcare and transport costs as it considered how to relieve poverty among beneficiaries.