Stormont has so far not put in place changes to benefits that have been implemented in other parts of the UK.
This has led to fines from the government.
Justin Welby told BBC Radio Ulster that there should be extra help to assist people here out of poverty.
"Should Northern Ireland itself be a special case?" he said.
"Yes it probably should, although not as a basket case or a charity case, but as a recognition of what has gone wrong in the past."
Secretary of State Theresa Villiers said the government continued to recognise Northern Ireland's special circumstances.
"That is why public spending per head is 23% higher here than the UK average," she said.
"When it comes to welfare reform Northern Ireland has much to gain from replacing a failed system that traps far too many people into dependency with a modern system that ensures work always pays."
The Northern Ireland parties had agreed on a welfare reform deal in December but Sinn FÃ©in withdrew its support in March.
Inter-party talks in Northern Ireland began in September in a bid to resolve the current political crisis at Stormont.
The two key issues being discussed are the impasse over welfare reform and paramilitary activity.
The Archbishop of Canterbury has said he believes Northern Ireland should be treated as a special case when it comes to the issue of welfare reform.