Iain Duncan Smith, the work and pensions secretary, was embroiled in a war of words with the archbishop of Canterbury after the head of the Church of England warned that planned changes to the benefits system will be damaging for children and families.

In his first significant political intervention since taking office, Justin Welby said capping benefits at below inflation would make children and families pay the price and he urged the government to support the most vulnerable in society.

Under changes championed by Duncan Smith, rises in welfare payments would be capped at 1% annually for the next three years as part of the government's austerity measures.

In a statement released by Lambeth Palace, Welby said: "As a civilised society, we have a duty to support those among us who are vulnerable and in need. When times are hard, that duty should be felt more than ever, not disappear or diminish. It is essential that we have a welfare system that responds to need and recognises the rising costs of food, fuel and housing.

"The current benefits system does that, by ensuring that the support struggling families receive rises with inflation.

"These changes will mean it is children and families who will pay the price for high inflation, rather than the government."

Duncan Smith hit back insisting that there was nothing moral about leaving millions trapped in dependency on the state. "This is about fairness," he said. "People who are paying taxes, working very hard, have hardly seen any increases in their salary and yet, under the last government, the welfare bill rose by some 60% to £200bn.

"That means they have to pay for that under their taxes, which is simply not fair," he told ITV News.

"There is nothing moral or fair about a system that I inherited that trapped people in welfare dependency. Some one in every five households has no work – that's not the way to end child poverty."

The shadow home secretary, Yvette Cooper, said the archbishop was right to speak out. She said Labour would like to see benefits rise with inflation, funded by restricting tax relief on pension contributions for the highest earners. "The government is just turning its back on all of this," she told BBC1's Andrew Marr Show.

Welby's comments came after 43 bishops wrote to the Sunday Telegraph warning the changes "will have a disproportionate impact on families with children, pushing 200,000 children into poverty". The letter, which has been backed by Welby and the archbishop of York, John Sentamu, urged the House of Lords to take action to protect children from the impact of the bill.

Duncan Smith has highlighted figures showing jobless benefits have risen 20% in the last five years, compared with an average 12% rise in private sector pay. But Labour, which opposes the 1% cap, says jobseeker's allowance has risen by 32% over the past decade, whereas wages have gone up by 36%.

The Children's Society says that, under the changes, a single parent earning £530 a week would lose £424 a year by 2015. A couple with two children, where one parent is working and earning £600 a week, would also lose £424 a year, according to its analysis.

The letter from the bishops says the change will "hit the poorest the hardest" by transferring the risk of high inflation from the Treasury to children and families.

Welby's intervention suggests he will not be discouraged from speaking out despite criticism of his predecessor, Rowan Williams, who was accused of meddling in politics. Among Williams's targets was David Cameron's "big society", which he suggested was aspirational waffle.

A spokeswoman for the Department for Work and Pensions said: "In difficult economic times we've protected the incomes of pensioners and disabled people, and most working age benefits will continue to increase [by] 1%. This was a tough decision but it's one that will help keep the welfare bill sustainable in the longer term.

"By raising the personal allowance threshold, we've lifted 2 million people out of tax altogether, clearly benefiting people on a low income."