"It was an extremely traumatic time for these people who struggled to find somewhere else to live, especially families with young children, and those with complex needs.
"We will have to work hard to regain their trust and we must ensure we deliver support services to those in need which is both sustainable and ongoing," she said.
Te Tuinga Whanau Social Support Services executive director Tommy Wilson said he commended the Government for doing "what's only right and fair".
Wilson said his service had worked with several families who had been evicted due to the testing.
"They were put under extra stress and financial hardship and the trauma they suffered on finding themselves homeless through no fault of their own cannot be underestimated."
Rotorua Budget Advisory Service manager Pakanui Tuhura said he applauded the Government for "taking this stand".
"We had a number, most who came from outside the district, including some from Auckland and Tauranga, who needed emergency housing after being evicted," he said.
"These clients were put under quite a lot of pressure and, understandably, they wanted to get out of living in motels and other temporary housing as soon as possible. "
Merepeka Raukawa-Tait, who chairs the North Island Whānau Ora Commissioning Agency, said she was pleased to see the Government taking steps to right a "grave injustice".
"What the Minister has put forward will go a long way to putting things right and the sooner the better," she said.
Social Development Minister Carmel Sepuloni said writing off debts and refunding money already paid back to the ministry was the "fair thing" to do.
"This Government is committed to ensuring people are accessing their full and legal entitlements and are treated with respect and fairness in the welfare system."
