The Health Service Executive (HSE) has been asked to compile a report into the administration of so-called "spare" vaccines to non-frontline staff.
Family members of staff at the Coombe hospital in Dublin were given excess doses of the Pfizer BioNTech vaccine earlier this month.
It later emerged that similarly, family members of staff at the Rotunda Hospital were also given excess doses after staff were able to reconstitute them from vials of the Pfizer vaccine.
On Tuesday, Minister for Health Stephen Donnelly said "what happened should not have happened", adding "It was a profound error of judgment; I'm not happy about it at all."
Mr Donnelly confirmed he would meet with the chair of the Coombe hospital on Wednesday morning following a meeting of its board on Tuesday.
“What happened was not acceptable,” he told RTE’s Primetime.
Earlier, Mr Donnelly also defended the level of information about the priorities of people who were to be vaccinated at the time the incident occurred, despite the fact that detailed descriptions of prioritisation of healthcare workers had been published only four days later.
“Any question as to whether family members should be vaccinated is fully covered off by the original protocol which has been up online for weeks.”
A spokesman for Mr Donnelly said the board had been asked for a full account of the incident and Paul Reid, chief executive of the HSE, had been asked to compile a short report on the question of vaccines being administered to non-frontline staff.
On Tuesday, Mr Reid said the incidents in the Coombe and Rotunda hospitals “don’t do any of us any good, or the programme any good”.
He told RTÉ radio: "Some of what we heard shouldn't have happened. I'm disappointed that they've happened. They are a small number of cases but I do appreciate they caused significant distress."
Prof Karina Butler, chairwoman of the National Immunisation Advisory Committee (NIAC), said the capacity to make up extra doses had led to the situation in the Rotunda.
The advice in such a scenario was to try to go through the prioritisation list, she said. “NIAC’s recommendation would always be to go through the prioritisation list to try to find people who would be suitable to get the dose.”
