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 26-year-old had been scheduled to play Louisa Chirico of the United States in round three on Wednesday, but pulled out during the warm-ups.
Belarusian Azarenka said she will have medical tests before deciding whether to play in Rome before the French Open, which starts on 22 May.
Her departure means the top five seeds are out of the Spanish tournament.
Agnieszka Radwanska, Angelique Kerber and Garbine Muguruza exited in previous rounds while fifth seed Petra Kvitova lost 6-3 6-4 to Australia's Daria Gavrilova on Wednesday.
Azarenka, who had recently won titles at Indian Wells and Miami, said she "tweaked'' her back during her opening Madrid match against Laura Robson and that the pain persisted during her second round victory over Alize Cornet.
She follows world number world 13 Lucie Safarova - who had to withdraw earlier in the week with food poisoning - and British number one Johanna Konta who retired in the first round with a respiratory illness.
The men's event also lost Roger Federer - the world number three another player out with a back injury.
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Since docking with the ISS in a Soyuz craft in December, the 53-year-old station commander has kept hundreds of thousands of followers back on Earth informed and entertained from orbit.
He has tweeted from the space station at least 1,500 times, capturing remarkable images of many corners of the world.
His first photograph came in his first tweet from the ISS: "Space Station! Floating free, buoyed up even more by my smile :)"
His first days were marked by a series of photos detailing life inside the space station.
But he soon branched out into striking orbital landscapes of the planet below.
We have collected just a few of Cmdr Hadfield's tweeted shots and captions here - more are available by browsing his Twitter feed @Cmdr_Hadfield.
A former fighter pilot, Chris Hadfield became a trainee astronaut in 1992 after winning selection from a field of 5,330 applicants, according to Nasa.
He flew on board the space shuttle, docking with the Russian space station Mir and as part of an assembly flight to the ISS in 2001.
He eventually won his own slot on board the ISS in 2010, training for his current mission until lift-off in December 2012.
After gathering hundreds of thousands of Twitter followers during his months on board, he made one final hit as the time came for his departure from the ISS.
He posted a striking video to YouTube of him performing a version of David Bowie's renowned 1969 hit song Space Oddity.
The video quickly went viral, and even prompted a response from Bowie's own official account: "Hallo Spaceboy..."
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.
[NEXT_CONCEPT]
Fourth seed Victoria Azarenka has joined the list of Madrid Open withdrawals with a back injury.
[NEXT_CONCEPT]
Canadian astronaut Chris Hadfield is due to return to Earth on Tuesday from a five-month stint on board the International Space Station.