Martin said he believes people will 'reflect' on benefits of vaccinating children and will bring their kids for jabs
Mr Martin also signalled that parents will be able to bring their children for vaccines from January 10.
The HSE is currently developing a plan to roll out vaccines for children aged as young as five.
During a press briefing in Government Buildings, Mr Martin said: "I think we will be recommending strongly that parents do facilitate their children getting vaccinated.
"But we understand the sensibilities involved.
"The high risk has started already in our hospitals in terms of the vaccination of children. It's started already.
"The next two cohorts will register from January 3 and then the January 10 (cohort)will be the majority of children," he added.
Mr Martin said there will be special vaccine facilities for children and people with expertise in dealing with children will be based in the centres.
He said he believes people will "reflect" on the benefits of vaccinating children and will bring their kids for jabs.
"One of the areas we are not yet clear about in terms of more research is needed is the long-term impacts of Covid on people generally and on young people also."
The Taoiseach said the roll-out of vaccines for children will have to be approached with "sensitivity".
He insisted there will be "very comprehensive information" for parents.
"The clinicians and doctors will be providing that information along with our public health leadership teams and that's the way we approach all vaccination programmes, particularly with children.
"I mean historically with vaccines, we've all experienced being vaccinated as children through a range of vaccines and vaccination programmes so it's not something new.
"My own view is that so far Ireland as a people - and I pay tribute to the robust debate within society which has been facilitated by media with the facilitation of different experts coming forward and so on - it has tended to land I think in a very centre ground of opinion which I think has informed the very high take-up of the vaccination so far amongst the adult population," he said.