Parents For Justice, the organisation representing families who have discovered their deceased children's organs were retained without their consent, have called for the disbandment of the Dunne inquiry.
The inquiry, chaired by Ms Anne Dunne SC, was established by the Minister for Health, Mr Martin, in April 2000.
The parents' group withdrew from the private inquiry last October, calling for its establishment on a statutory footing. It was concerned it would not be able to link names to actions.
The parents' latest call for its disbandment follows weekend reports that Ms Dunne had written to the Minister for Health, Mr Martin, saying Parents For Justice did not represent all the families involved and that her inquiry could proceed with its work.
Ms Dunne said she had received 407 submissions and that approximately one-third of these were from families who were not members of Parents for Justice.
Ms Fionnuala O'Reilly, spokeswoman for the group said she was "incensed" by Ms Dunne's claims.
"We have already withdrawn co-operation from the Dunne inquiry because it is incapable of doing its job properly without being on a statutory basis. This inexplicable outburst by Ms Dunne serves only to prove out point that this inquiry is now a spent force and should be wound up immediately," she said.
She said the group had not seen the full text of Ms Dunne's letter to the Minister but voiced its concern "about its tone and the obvious attempt by Ms Dunne to discredit Parents for Justice".
"In view of her letter to the Minister and the views expressed, we feel that Ms Dunne is no longer impartial enough to run an inquiry into such an important matter. We therefore request the Minister for Health to disband the present inquiry and initiate a full and proper public inquiry into this scandal as a matter of urgency," she said.
A spokeswoman for the Department confirmed Ms Dunne had written to it last month but said the position of the Minister remained as that of December 18th last, when he met representatives of Parents for Justice.
He told the group then that having met Ms Dunne, she had told him she would be able to provide a report of her inquiries by the end of this year.
"In light of these discussions," the spokeswoman said, "the Minister was of the view that the inquiry as established should continue."
She said Ms Dunne had at that point already considered in excess of 150,000 pages of documentation, contacted Government departments, State agencies and pharmaceutical companies and had visited hospitals. She had also received assistance from coroners.
"The position is that she [Ms Dunne] should be allowed to finish her work, submit her report and then there will be an opportunity to consider any other option," the Department spokeswoman said.