Fianna Fáil's Health Spokesperson Billy Kelleher has said the operation of the discretionary medical card system is not humane at the present time.
Mr Kelleher said people who had discretionary medical cards for many years were now having them withdrawn, despite the fact that they had not experienced a change in either their illness or their income level.
Speaking on RTÉ's Today with Sean O'Rourke, he criticised the Government's plans to introduce free GP care for children under six, while at the same time removing medical cards from those who are chronically ill.
He said: "People who have the most appalling conditions, diseases, illnesses, incapacity are having them (medical cards) withdrawn and that is something I cannot get my head around at the present time."
Minister of State for Primary Care Alex White said only a Universal Health Insurance system will correct the current system.
Speaking on the same programme, Mr White said that the allocation of medical cards should not be done on a "grace and favour basis", but by a transparent system that people understand.
Such a system should afford flexibility to people where possible, he said.
Minister White said that in the meantime the Health Service Executive can only issue medical cards, not on the basis of an illness or condition, but on the basis of means as has been the case under law since 1970.
He would not criticise historic decisions where authorities acted "humanely" at a local level to secure a discretionary medical card for people with specific medical needs.
However, he said that this situation could not continue and the key was to improve services for people and improve access to disability services, hospitals, equipment and therapies.
Outside of the regular means test, Mr White said people could apply on a discretionary basis for extra expenses incurred as a result of a medical condition.
He said a "third tier" of medical card based on medical condition would require new legislation.
Speaking during Leaders' Questions today, Fianna Fáil leader Micheál Martin raised the appearance of two carers, Declan and Annette Coyle, on The Saturday Night Show, whose son Alex had his medical card removed.
He said that this captured the scandal going on in relation to the decision to end discretionary medical cards.
Mr Martin asked Taoiseach Enda Kenny if he would intervene and restore medical cards to those who have had them taken from them.
In response, Mr Kenny said that he had not seen the show and did not want to talk about individual cases.
Mr Kenny said that the centralisation of the scheme meant that they were applied "across the board" and he questioned how far you can push that discretion given differing income limits.