The Saint John of God Order has criticised Minister for Health Simon Harris after he called on it to repay money intended for disabled service users which was given to senior executives.
The order says there is no reference to any diversion of funds in a HSE audit of the brothers' disability charity.
The Health Service Executive told RTÉ News the order owes some €7m to the charity.
Last month, a draft HSE audit of the St John of God Community Services charity revealed that its founding order paid millions of euro in top-ups to at least 14 executives.
The charity had disregarded a government instruction in 2013 to abide by public pay norms.
Now the HSE has completed the audit and says the order owes the charity millions of euro.
Geraldine Smith, the Assistant Director of Internal Audit at the HSE, has said there are two sums of money owing due to the overpayments.
Firstly, executive compensation payments amounting to €1.83m which she is recommending the board of the St John of God Services seek to recoup from the 14 beneficiaries.
Secondly, she says the order should pay to the St John of God Community Services €7m-€9m for services that it got from the charity when individual managers were performing services for the order, sometimes at locations abroad.
"The most important (refund to SJOG Community Services) is the value of those managers' services that were essentially funded by the taxpayer," she continued.
Meanwhile, groups representing parents and friends of service users at one of the services' largest centres have echoed the call for the St John of God Order and the 14 executives to repay the money.
Liam McNamee, chairman, St Raphael's Parents' and Friends' Association, said the order is morally obliged to do so.
He said the managers who benefitted have a similar obligation to ensure they are doing things properly.
This morning he and his committee were derigging marquees used at yesterday's 52nd garden fete at the St Raphael's complex in Celbridge, Co Kildare.
Up to €200,000 has been raised by the Parents' and Friends' Association through this and other ventures such as their second had clothes shop.
The funds are managed independently of the services company.
The association is calling on the St John of God Order to pay the money that is owed to its associated charity.
Also in Celbridge, Aisling McNiffe said the Parents' Association at St Raphael's Special School had complained SJOG Community Services to the Charities Regulator.
"The people receiving services ... should be given the best possible help but the services have not been doing that.
"They're a charity that have not been doing their job," she said.