Peter Robinson has called for immediate action to compensate abuse victims after payments recommended by a inquiry were delayed by Stormont's collapse.
The ex-first minister suggested seeking "consensus" from political parties that could allow the payments to be set up in the absence of devolved government.
The Historical Institutional Abuse (HIA) Inquiry recommended a state apology and compensation for victims.
But the collapse of Stormont in January meant the process was put on hold.
Writing in the Irish News, Mr Robinson said the abuse of victims in children's residential homes was an "appalling and vile chapter" in Northern Ireland's history which had been "swept under the carpet for too long".
"Having been the helpless victims of sexual exploitation and ill-treatment , they have lived lives as the victims of society's denial, disinterest or apathy and now they have become the victims of political stalemate."
The former DUP leader added he believed there would not be "much contention" among Stormont parties if Secretary of State James Brokenshire were to act on the HIA Inquiry's recommendations "immediately".
When he was first minister, Mr Robinson helped to set up the inquiry, along with the late deputy first minister, Martin McGuinness.
Led by Sir Anthony Hart, it examined allegations of abuse in 22 homes and other residential institutions between 1922 to 1995.
The inquiry concluded there was widespread abuse and mistreatment of young residents in the institutions run by churches, charities and the state.
Mr Robinson said he had hoped "immediate apologies and compensation would follow" and he criticised "the lack of urgency" in paying compensation.
"The victims of institutional abuse have waited an inordinately long and unacceptable time for the truth to be revealed, recognised and a measure of reparation to be made," he said.
He added that he and Mr McGuinness met victims of abuse on "several occasions".
"Compensation was not top of their agenda, but Martin and I recognised that there had to be a financial aspect to any just outcome of this appalling and vile chapter.
"Both Martin and I were deeply affected by their stories. There is nothing 'historic' about this abuse. The victims live it every day.
"The victims wanted the opportunity to tell their stories and needed an apology for the suffering they had endured," he said.
He said a tax-free lump sum payment should be made to all survivors, including in homes and institutions that were not covered by the inquiry.
Mr Robinson called on Mr Brokenshire to meet political parties on the issue "and assess whether at least on this outstanding matter there is sufficient consensus to proceed in all or part with the implementation".
"Justice and humanity demands action," he added.
Sir Anthony Hart's recommendations
- Compensation to survivors of abuse, including in homes/institutions not covered by HIA inquiry, and relatives of deceased
- Permanent memorial erected at Stormont
- Public apology to survivors
- Establishment of a commissioner for survivors of institutional abuse
- Specialist care and assistance tailored to needs of victims
Mr Robinson's comments come after the death of victim of abuse, Billy McConville, whose mother Jean McConville was murdered by the IRA in 1972.
After the abduction of the single mother of 10, Mr McConville was taken in care.
He told the HIA Inquiry he was abused by some De La Salle Brothers and physically abused by a lay teacher in Rubane House in County Down.
His funeral is due to take place on Wednesday at St Paul's Church in west Belfast.