Taoiseach Micheál Martin says administering the Covid-19 vaccine will be "huge" and cannot be rushed.
The Covid-19 vaccine from Pfizer and BioNTech has been approved in the UK, paving the way for vaccination to start next week.
Ireland currently has a vaccine taskforce, which has met twice and will report to the Taoiseach on December 11 on how Ireland should roll out the immunisation programme.
The Taoiseach has repeatedly rejected Labour's suggestion of creating "a national standing group with a minister in charge" or nominating one person with full responsibility on the vaccine due to the enormous work it will take to roll the vaccine out throughout Ireland.
Alan Kelly said the country needs to "have a database in relation to who gets the vaccine, who doesn't get the vaccine, underlying illnesses, age, and everything".
What we need from the government— The Labour Party (@labour) December 2, 2020
the number of vaccines available
who will get the vaccine first and in what order
how the vaccine will be stored
will be an IT infrastructure behind the distribution
if there is a public health campaign ready
Watch @alankellylabour here👇 pic.twitter.com/RE0rM5Obge
The Taoiseach said, during Leader's Questions, that the programme cannot be rushed and naming one person would not be effective in practice.
"This is an issue of national priority which was the very top of government and I will stay on top of this until we get everything sorted.
"Let's be clear: a lot of the experience and expertise resides in the Department of Health, the HSE, that had been involved in previous vaccination programmes," he said.
"There's a lot of residual expertise and experience there to draw upon.
"Just for the information of the house, Pfizer BioNTech, sought market authorisation yesterday from the European Medical Agency and Emer Cooke (EMA Executive Director), an Irish person, briefed health ministers this morning, and they will assess the Pfizer BioNTech vaccine, on the 29th of December at the latest. Maybe before that.
"I think it's very very important notwithstanding what happened in the UK yesterday, that the responsibility on that authority is huge, in terms of recommending a vaccine as being safe and effective.
"We shouldn't in any way create a pressure zone on the regulatory authority to do the right thing here."
Mr Martin also provided a brief update on the work done to date in terms of readying the country for the vaccine.
"In terms of the work of the task force, work is proceeding at pace, yesterday delivery was taken of up to nine ultra-low (temperature) fridges trucks into the country, stored at (Dublin's) City West," he said.
"The fridges will be commissioned by the middle of next week and then they have to be distributed within five days from the central depot when a vaccine ultimately arrives here.
"The potential logistics of this is a key work stream and the IT infrastructure, an entire database will have to be created in terms of who gets what, the workforce, who administers the vaccine, because of the scale of this it will be more than just the normal workforce that would apply and administer a vaccine."
The Taoiseach said it would be "easy to nominate a name" but it would not do more than the taskforce already is.