The Minister for Health and Children, Mr Martin, could face High Court action if he does not announce a full tribunal of inquiry into the organ retention scandal in the next seven days.
The ultimatum has been issued by the organisation representing families of deceased children whose organs were retained and disposed of without parental consent since 1970.
Some of the State's biggest hospitals including St James's, St Vincent's, the Rotunda and Holles Street are implicated in the scandal.
Parents for Justice say the Department of Health and Children had frustrated their efforts to get full dislosure about the scandal by failing to engage in "substantive communication" .
Chairperson Ms Fionnuala O'Reilly said today: "We've already given the Minister and the Dunne Inquiry more than enough time to resolve this issue and get to the bottom of the scandal which has plagued our lives for far too long. But they have dragged their heels and we believe we have been far too nice for too long."
Currently, a private inquiry is being conducted by Ms Anne Dunne SC, but plans to also bring the investigation into the public domain through a Dáil committee hearing have been ruled out because of a Supreme Court decision in April. The Dunne Inquiry began in March 2001.
The Supreme Court found an Oireachtas committee could not conduct an inquiry which could lead to adverse findings against citizens which would impugn their good name. It followed a legal challenge to a joint Oireachtas sub-committee inquiring into the shooting dead of John Carthy in Abbeylara, Co Longford, by members of the Garda.
Parents for Justice say that, in light of the ruling, the only way to get full disclosure is for the Dunne Inquiry to be set up on a statutory basis.
Solicitors for the organisation wrote to the Department in August calling for a full tribunal but say they have not received a constructive response.
Ms O'Reily said today that if Mr Martin does not announce his intention to give the Dunne Inquiry statutory powers in the next seven days then legal action could follow.
"We're ruling nothing in or nothing out. At least I think we would be considering High Court action.
"It's a very sad state of affairs if families have to be taken to the courts to get answers to legitimate questions," she said.
Parents for Justice, which was set up in December 1999, will hold its a.g.m. for its 2,000 strong membership in November but a meeting is planned for the weekend after next at which the minister's reposnse will be considered.
Among its members are around 200 people whose adult relatives had organs retained without consent.