All children aged 5 to 11 can be registered for the Covid-19 vaccine on the Health Service Executive website from today.
Dr Lucy Jessop, Director of Public Health at the HSE's National Immunisation Office, said "several thousand" parents have already made an appointment for their children since the booking portal opened this morning.
"That's really good news that parents are coming forward, but obviously parents need to take time to look at the information," she told RTÉ's News At One programme.
Dr Jessop urged parents to talk to a medical professional if they have any concerns.
She added: "There's also a cartoon that we've done so you can explain the vaccination process to your child so they feel comfortable when they come in to get the vaccine."
Children who have had Covid-19 can still get the vaccine, but must wait for a month after their positive test, Dr Jessop said.
There must also be a two-week interval between the Covid-19 vaccine and other immunisations, she added.
"As a precaution, the National Immunisation Advisory Committee has advised that children should wait at least 14 days between having a vaccine and having the Covid-19 vaccine."
Parents should receive an appointment for their child a couple of days after registration.
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Parents will need need a Personal Public Service (PPS) number, Eircode, mobile phone number and an email address to book a vaccine appointment for their child online.
Alternatively, parents can call HSE Live on 1800 700 700 to register their child over the phone.
The Pfizer vaccine for children is a smaller dose than the vaccine for adults. They will need two doses about three weeks apart.
Most children will be vaccinated at a vaccination centre near their home. They will need to be accompanied by an adult. Children attending alone will not be vaccinated.
Meanwhile, the booster vaccine programme opened to all those aged 16 and over from yesterday - a week earlier than originally planned.
Appointment-based clinics for those aged under 30 years are taking place in designated vaccination centres.
GPs will continue to vaccinate down through the age groups, by appointment. Pharmacies will also continue to vaccinate people by appointment.
Meanwhile, the Government is set to consider reducing the self-isolation period from 10 to five days for some people who test positive for Covid-19, according to the Green Party leader.
Minister for Transport, Eamon Ryan, said these changes would impact those who test positive for Covid-19 if they are asymptomatic or their symptoms are resolving.
The Government may also reconsider the rules around isolation for close contacts.
The Department of Health was today notified of a further 16,986 cases of Covid-19.