Troubles and HIA schemes could cost up to £60m
A compensation scheme for historical abuse survivors and the pension for Troubles victims could each cost between £25m to £60m, First Minister Arlene Foster has said.
Westminster passed laws last year that provide for both schemes to be set up.
They will be administered by the Stormont Executive.
Mrs Foster said the costs cannot be absorbed within the existing Northern Ireland budget.
She told a Stormont committee the source of funding for both areas would have to be confirmed as a "matter of some urgency".
Mrs Foster and deputy First Minister Michelle O'Neill were appearing before the committee that scrutinises the work of the Executive Office.
Mrs O'Neill said some institutions and churches needed to contribute to the funding for the scheme, and that the Executive Office hoped to "move at pace" to progress this.
"How do we make others play their part in this, we've just received the list of all the organisations involved and we'll go and have to engage with them ourselves," she told MLAs.
On Friday, the government published the legislation that will provide for the Troubles pension to be established.
A judge-led board will decide who will qualify for the new scheme for people who were injured during the Troubles.
Payments will range from £2,000 to £10,000 every year for the rest of a victim's life.
There will also be provisions to extend payments to those who care for Troubles victims for more than 35 hours a week.
In the event of a Troubles victim's death, there will be provisions to make a payment to their loved ones.
The compensation scheme for victims of historical institutional abuse was set up following legislation passed at Westminster last October.
It had been delayed due to the collapse of devolution at Stormont in 2017.
An inquiry had investigated historical allegations of child abuse at 22 residential institutions run by religious, charitable and state organisations across NI in a 73-year period.
It had recommended that all victims of institutional abuse should receive tax-free, lump sum payments ranging from £7,500 to £100,000 from a government-funded redress scheme.
A commissioner is also due to be appointed.
Last week, the head of the civil service David Sterling said the redress board that will oversee the payments has been set up, and that it is hoped survivors can begin to receive the first payments by the end of March or start of April this year.
Elderly and gravely ill victims are to get priority for the compensation payments, with an initial acknowledgement payment of £10,000 given to qualifying claimants.