A Cork TD believes the Master of the Coombe should resign, following revelations that a doctor at the hospital took home vaccines to his family members.
The hospital apologised earlier this year after it emerged that 16 family members of employees were vaccinated.
An independent review published yesterday found that in the case of one family, the vaccines were brought off-site to be administered.
The hospital board says "lessons must and will be learnt" and that it has "started a process to address the implications".
On Newstalk Breakfast, Deputy Holly Cairns was asked whether the master - Prof Michael O'Connell - should resign.
She said: "Yeah, I think there needs to be accountability.
"Why would somebody get a vaccine ahead of the cohorts that need it?"
She said the Coombe incident - as well as the recent revelations around how leftover vaccines were administered at the Beacon Hospital - 'damage confidence' in the vaccine rollout.
Maternity hospital restrictions
Separately, Deputy Cairns says restrictions around partners attending maternity hospitals need to be reviewed and addressed 'immediately'.
She says couples currently face a 'geographical lottery' when it comes to the rules around individual hospitals.
Restrictions have been in place across Ireland's maternity hospitals for over a year now, with different rules often in place depending on the hospital.
In the Dáil yesterday, Health Minister Stephen Donnelly said he 'fully agrees' there should be as much visitation as possible once it is deemed safe by 'local clinical leads'.
Tánaiste Leo Varadkar, meanwhile, suggested 'bringing unvaccinated people into a hospital is a risk'.
Deputy Cairns said the different answers from different ministers have brought no clarity.
She said: “For some reason, the Minister for Health said yesterday in the Dáil that it now depends on each individual hospital.
"However, I asked the Taoiseach about it in September and multiple times since then… and he said there should be a national approach in relation to this.”
Deputy Cairns said women could go through 24 hours of labour before they get to a stage when a partner is allowed to attend - and noted that partners are already a close contact of the woman before they even arrive in hospital.
She also said she's heard from many first-time mums in particular who are terrified of going through the experience of their own.
She said: “Parents have a right to be at the birth of their own child.
“Now the frontline healthcare workers have been vaccinated, what I really want is for this to be revisited and addressed immediately.
"They’re calling them visitors, and I think it’s clear you’re not a visitor at the birth of your own child. It’s fair to want to be there."
She pointed out that the HSE has already reclassified partners as an essential accompanying person for the 20-week scan - but that's still not the case for later scans and most of labour.
She also suggested the likes of rapid antigen testing could be used to ensure partners can safely access maternity hospitals.