Representatives of Parents for Justice (PFJ) walked out on the minister after he told them he would not put the present post-mortem inquiry on a statutory footing at this stage.
Mr Martin told PFJ representatives he wanted the Dunne inquiry in to why hospital kept the organs of dead babies to continue.
He said he was always committed to a two-stage inquiry.
The minister also told the parents he would not make a decision as to whether the second phase would be statutory or non-statutory until the first phase was completed.
PFJ is the support group for more than 800 families who discovered their deceased children’s organs were removed and retained by hospitals without their knowledge or consent.
Mr Martin told them he had met with inquiry chairperson Anne Dunne SC, who informed him she would be able to provide him with a report on the removal, retention and storage of organs in all paediatric hospitals in 12 months.
The minister said the inquiry had already considered more than 150,000 pages of documentation submitted by participants.
The Dunne post-mortem inquiry began in March 2001 and to date has cost the State €5.3 million.
PFJ spokesperson Fionnuala O’Reilly said they walked out on the minister 10 minutes into their meeting with him.
“His position on the issue was entrenched. There was no room for negotiation. His attitude towards us was very hostile,” she said.
Ms O’Reilly said Mr Martin was not fit to continue as Minister for Health and Children because he did not want openness and transparency into one of the State’s major health scandals.
“The minister has made a mistake today of Noonanesque proportions which inevitably will have long-term implications for his political career,” she said.
PFJ intend to hold intensive consultations with their legal team. Ms O’Reilly said they were planning an “aggressive” series of actions that would highlight the extent of the scandal.
Because of a confidentiality clause it is not known how many parents are still co-operating with the inquiry.
In early October, PFJ walked away from the Dunne Inquiry and at their EGM last November 30 all their members agreed to request the return of all personal documents submitted to the inquiry.
Ms O’Reilly said the minister’s position had compounded the grief of the families involved, especially at this poignant time of year. Some of the families at the centre of the scandal staged a silent vigil outside Leinster House while the meeting took place.
“Those people have horrific stories to tell. Entire babies have disappeared in this scandal,” Ms O’Reilly said.