The Inquiry into Historical Institutional Abuse Bill passed its second stage, on 25 June 2012.
The inquiry, which will be headed by retired High Court judge Sir Anthony Hart, will examine allegations of abuse at children's homes, care institutions and borstals between 1945 and 1995.
William Humphrey of the DUP said he wanted the findings of the inquiry to be released as soon as possible.
"We must make sure that victims and their families address their grievances, expose wrongdoing and are provided closure if indeed closure is possible," he said.
Sinn Fein's Alex Maskey said he hoped any abuse people endured would be exposed, and explained that the legislation would allow for recommendations to be brought forward.
The SDLP's Conall McDevitt described this as a "terrible, terrible period in our history" and said the inquiry would bring some "sense of truth and justice" for individuals affected.
He said he recognised there were many who had suffered "at the hands of abusers within the community" and although this inquiry did not cover clerical and child abuse outside of institutions, they were as entitled to an inquiry.
Ulster Unionist John McCallister said there was some need to restrict the time limit of the inquiry but highlighted that he did not want this to limit or "hinder the search for truth".
Chris Lyttle of the Alliance Party said some victims were concerned that there was no provision after 1995.
TUV leader Jim Allister said he felt the bill "came up short" due to its only investigating institutional abuse meaning that "clerical abuse is outside its ambit".
Responding to the debate, Junior Minister Jonathan Bell, said victims and survivors had been consulted throughout the process.
He said many had said they wanted the inquiry to be about acknowledgement and not compensation.
Mr Bell addressed concerns over the inquiry stopping at 1995 and explained that since this year all children's homes have had to act "within an established regulatory framework" meaning that improved safeguards have been in place.
The first part of the debate can be viewed