Tánaiste Eamon Gilmore has told the Dáil that the Government is seeking legal advice on its options with regard to the Mobility Allowance.
It follows a report from the Ombudsman that found the Department of Health has been illegally operating the scheme for the past 12 years.
"It is not the Government's wish to withdraw the Mobility Allowance from those who currently receive it," Mr Gilmore said in response to questions from Sinn Féin.
"The Government is seeking legal advice as to how we can proceed in a way that is reasonable, sustainable and does not cause undue distress to those in receipt of the allowance."
The report, Too Old to be Equal, says the department has known about this illegality since at least 2008. However, despite agreeing in April last year to remove an illegal upper 66 years age limit, it has failed to do so.
The department said acting on the Ombudsman's recommendations would create liabilities the State cannot afford.
The Disability Federation of Ireland has said it is "extremely worrying" that the department continues to act outside of the law by illegally operating the scheme.
DFI Chief Executive John Dolan said the fact the department acknowledged the issue and then rowed back on taking action is of concern.
Mr Dolan said it is clear that the department is only worried about upsetting the Budget arithmetic, but he said it has an obligation to support and look after people.
The Government did not learn anything from the controversy last September when cuts were imposed to personal assistant hours and later had to be reversed, he claimed.
'Politics clashing with bureaucracy'
Speaking on RTÉ's Morning Ireland, Emily O'Reilly said she had no sympathy for the department and believed this could be a case where "politics is clashing with the bureaucracy".
She said: "They could move immediately to act within the law.
"They have to remove the upper age limit and if there is a financial difficulty that I think perhaps they have to make the scheme tighter."
The Mobility Allowance is a monthly payment made by the Health Service Executive to people with a severe disability, who are unable to walk and who would benefit from trips away from home.
It has been in place since 1979 and is worth a maximum of just over €208 a month.
Ms O'Reilly said that this month the department rejected a further recommendation from her to drop the limit, after five new complaints from people refused the allowance.
In the report, she says the continued disregard of the law by a key State body is quite "unacceptable" and she has now reported it to the Dáil and Seanad.
The report says the Ombudsman understands that the position being put forward by the department is a position agreed with the Minister for Health.
It details five cases of refusal, including a case where a complainant was aged 81 and who died last March.
The department said it cannot amend the scheme as it would ignore the serious financial constraints on the department, the HSE and the State.
It also warns that the scheme cannot continue to operate on its present basis and the department must consider a further number of issues that have arisen from recent approaches to Government in this matter.
The upper age limit applies to those first applying after 66 years.
Allowances must be based on need - ALONE
An organisation representing older people has said the Government must provide allowances on the basis of need, regardless of the financial situation.
Responding to the Ombudsman's report, the chief executive of ALONE said a Government department operating outside the law was a "dangerous precedent."
Sean Moynihan said the issue of older, disabled people being able to get out of their homes is a very important one.
"What we believe is that regardless of how much money is available, there should be equality for health services and for allowances, based on need and assessment, not based on age," he said.
"If anybody in any Government department feels that something they're doing is outside the law of the land...the fact that they feel they can proceed with that is a very dangerous precedent when we're in a time of cuts and... redistributing what money we have."