It is thought hundreds of people across the region could come forward with their claims of abuse if a new investigation is established, or the current inquiry amended.
Children who were abused by clerics in the community, and women over 18 who were in homes such as the Magdalene Laundries, where they suffered institutional abuse, do not fall under the existing Historical Institutional Abuse inquiry.
But on Wednesday, they gathered to ask for the terms of that inquiry to be extended to include them.
They are backed by Amnesty International, and Patrick Corrigan from the organisation said it is now time for NI's politicians to take further action.
He explained: "We are now coming to them with those other issues too, particular groups who have been left out of the current inquiry - children who have been abused at community or parish level, and women who were incarcerated effectively in those Magdalene Laundry-type institutionsand who suffered abuse, not as children, but as adults.
"It's now time for the Executive and the Assembly to turn their attention to justice and truth for those groups too."
Many of these people are now in advanced years and they've had to live with shame, with stigma and they've a dark shadow cast over the whole of their lives, and a feeling that nobody wanted to know them and nobody was there when they were most vulnerable in their lives.
Patrick Corrigan, Amnesty
For the victims of abuse, Mr Corrigan said they want the state to acknowledge "the pain they went through".
He added: "They now want to turn to our political representatives, and we are asking today for those leaders to listen to those victims now as adults and to give them the truth, the justice and the acknowledgement that they crave before they finally pass away themselves."
SDLP MLA Conall McDevitt said all victims of abuse have the right to be told the truth.
"The need to get to the bottom of what went on in the Magdalene institutions, the needs to provide justice for those women, is every bit as great as it was for the children who were abused in institutions," he said.
But UUP leader Mike Nesbitt believes there is a political reticence to begin another inquiry into abuse.
"I've sensed on occasion, and I'm speaking personally, that there is a lack of political will to broaden it out to make sure everybody who was abused gets a process, gets the opportunity for truth, justice and some sort of recompense or redress," Mr Nesbitt said.
"Some people think they would like some money to compensate for what happened to them. Others understand that they need support, they need services to tackle particularly mental health and wellbeing issues, and I think that's only fair."
The question is - do we have the political courage to give justice to these women, whether they were children or whether they were young adult women, and give them the same sort of opportunity for closure that we are giving the survivors of institutional abuse.
Conall McDevitt, SDLP
The current inquiry is investigating allegations of abuse at 35 sites across NI, including state-run children's homes, institutions run by the Catholic Church, borstals, and institutions run by Protestant churches or voluntary sector organisations.
The three-year review, chaired by Sir Anthony Hart, could cost up to £19m.
After hearing from the alleged victims, an acknowledgement forum panel will produce a report to Sir Anthony detailing the claims.
Earlier this year, Taoiseach Enda Kenny described the Magdalene Laundries as "the nation's shame".
Speaking in the Irish government, Mr Kenny apologised to the victims of abuse after a report found thousands of women forced into the workhouses were physically and verbally abused.
The 18-month inquiry found 10,000 single mothers, women, and girls as young as 11 were forced into detention, mostly in the for-profit laundries. More than 2,000 women were sent to the laundries by the Irish authorities.
Some were detained for petty crime, others for disability, or pregnancy outside marriage.