Groups representing families at the centre of a spinal surgery controversy have said they are willing to engage in further discussions around the terms of reference of a HSE-commissioned review into orthopaedic surgery at Temple Street Children's Hospital.

Speaking after the conclusion of a meeting this evening at Government buildings, Amanda Coughlan Santry of the Spina Bifida and Hydrocephalus Paediatric Advocacy Group, said that they would consider sitting down with the orthopaedic consultant leading the review, Selvadurai Nayagam.

However, Ms Coughlan Santry said that it remained the case that they were not "trusting of the process".

Families also called for a taskforce to be established to improve spinal surgery waiting lists and other care services.

A spokesperson for Taoiseach Leo Varadkar described the meeting as "an open and honest exchange of views", adding that Mr Varadkar committed to further engagement.

Both the Minister for Health Stephen Donnelly and Chief Executive Officer of the HSE Bernard Gloster also attended today's meeting.

Separately, Mr Donnelly is due to meet with the expert leading the review, Mr Nayagam, to have preliminary discussions around the investigative work that he will conduct.

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Earlier, Mr Varadkar said he shares the anger and frustration of families impacted by long waiting lists for paediatric spinal surgery.

Speaking ahead of the meeting with groups representing families affected by poor surgical outcomes, Mr Varadkar said that despite investment in recent years, waiting times have not improved.

The Taoiseach said the main focus of the meeting was to hear the concerns of families, who threatened to boycott a HSE-commissioned external review into aspects of orthopaedic surgery at Children's Health Ireland (CHI) at Temple Street in Dublin.

At their press conference this afternoon, the groups said that they had lost confidence in the HSE, CHI and Mr Donnelly.

The families of children with scoliosis, spina bifida and hydrocephalus also said they would not cooperate with the review it its current format.

They called for significant changes to the review's terms of reference, saying they will not allow their children's medical records to be used by the inquiry if they are not happy with the terms.

They also said that Liverpool-based expert Mr Nayagam, who is to conduct the review, should be removed as he is not a spinal surgeon.

The families said that a taskforce should be established to address the care provided to children in need of spinal surgeries and the long waiting lists for operations.

Yesterday, the CEO of CHI described its use of unauthorised springs as implants in children as a "truly shocking" and an "unprecedented occurrence".

Eilísh Hardiman said there had been "a shocking litany of events" at CHI that were "distressing".

She told the Oireachtas Health Committee that staff are "distraught" at the death of ten-year-old Dollceanna Carter following spinal surgery at Temple Street hospital.

Tánaiste Micheál Martin has repeated his "shock" and said there must be a "comprehensive account" of what occurred.

Speaking in Cork, Mr Martin said: "I am very shocked by what has transpired. What is important is that an external review takes place and that we get a full complete and comprehensive account of what has happened."

"What has struck people the most is the apparent utilisation of equipment or devices that are not of medical grade standard or did not go through the proper certification processes. I find that quite extraordinary and very difficult to comprehend. That certainly needs a comprehensive explanation."

Mr Martin said the families had experienced a breakdown in trust in relation to their dealings with the hospital.

"Trust is eroded, and confidence is eroded. Above all what we all have to do in terms of provision of health services is to develop services that people have trust and belief in and above all deals with, as best as one can, with particular conditions that people would have and children would have on an ongoing basis."

Additional reporting Sinead Spain