Published Thursday, 13 June 2013
They were joined by victims of clerical child abuse at Stormont Castle on Monday.
Neither group is included in the current Historic Institutional Abuse inquiry, which is investigating claims of mistreatment at 35 sites across Northern Ireland.
The campaigners, along with Amnesty International, discussed their calls for a new inquiry with Jonathan Bell and Jennifer McCann.
Michael Connolly is part of the Clerical Abuse NI campaign. As a child, was abused by a priest in Co Fermanagh.
He said: "I would not want to raise the expectations of clerical abuse victims throughout Northern Ireland, but I did take away from that meeting quite a positive response.
"The message that they have received, I hope, will go back to the first and deputy first minister's office and we will get a very urgent, positive response from them."
Mr Connolly said a fresh inquiry could cover hundreds of victims, many of whom are now elderly.
Any delays to an inquiry mean they may not see the outcomes, he told UTV.
He added: "The inquiry could be four or five years down the line. It has got to take place now. It has got to be initiated now."
Amnesty International's Patrick Corrigan said they went into the meeting with a clear message.
"While [the ministers] were unwilling to make any commitments to deliver inquiries, we made it very clear that no abuse victims should be left behind.
He explained: "The ministers committed to reviewing the need for an inquiry into Magdalene Laundry-type institutions, and that they would report back to us in the coming week after discussing it with their Executive colleagues."
He reiterated Mr Connolly's calls that an inquiry must happen sooner, rather than later.
"On the clerical abuse victims we made it clear that victims were unwilling to be patient to wait until 2016 and beyond for the Executive to consider their need for an inquiry.
"That's too long to wait for victims who are not covered by that inquiry.
Mr Corrigan added: "We've asked them to reconsider their position and to deliver an inquiry that will look into clerical abuse in the community."
The Historical Abuse Inquiry is investigating cases involving children in residential institutions in Northern Ireland since 1922.
© UTV News