Almost half of all Covid tests carried out last week involved children, according to the Health Service Executive.
It comes as the Department of Health today reported 1,346 new cases of Covid-19.
The number of people in hospital with the virus is now 315, up four since yesterday. Of these, 59 are in intensive care, up one since yesterday.
HSE Chief Executive Paul Reid said that 45% of Covid-19 tests carried out in the past week were among those aged between 0-18 years.
However, he said that transmission rates in schools remain lower than in the community.
Speaking on RTÉ's This Week programme, he said the best thing for children is for them to remain in school.
Mr Reid said that 12,000 children out of school as close contacts is a relatively small number out of one million school children.
Earlier, infectious disease consultant Dr Clíona Ní Cheallaigh had said that "a lot of" children aged under 12 could have coronavirus by spring.
Mr Reid, when it was suggested to him that most pupils may contract Covid-19, said the HSE does not expect this will happen.
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The Chair of the National Public Health Emergency Team Epidemiological Modelling Advisory Group said that concerns about Covid spread in schools are based on an uncritical interpretation of modelling from the US, which depends on an unrealistic scenario.
A lot of commentary saying that most or all schoolchildren will be infected with SARS-CoV-2 in the coming months, based on an uncritical reading of this modelling study. It is highly unlikely that the scenario modelled will happen in the real world. 1/12https://t.co/AlMbCNWgK8 pic.twitter.com/tNrQtZfEQh
— Professor Philip Nolan (@President_MU) September 12, 2021
Professor Philip Nolan, writing on Twitter, said that the model depends on assumptions which are very different to the real-world experience of the virus.
He said that the average reproductive number of the virus in schools is below 1, though this may rise due to the Delta variant spreading more easily than previously dominant variants of the virus.
Prof Nolan said "increased transmissibility of Delta might bring in-school reproduction number above 1, making it more challenging to manage outbreaks, so it is prudent to be conservative in isolating close contacts until we are assured in-school transmission remains low with Delta".
Speaking on RTÉ's Brendan O'Connor programme earlier, Dr Clíona Ní Cheallaigh said modelling in the US shows that the Delta variant is highly transmissible and that without mask wearing in primary schools, the virus will continue to spread.
She said that mask wearing and better ventilation is needed in schools to prevent further spread.
"We need to face facts and have an honest discussion... to focus in on what kids need" to protect their health and education, she said.
While many children will not become very unwell, she said, a small percentage of children will experience severe illness.
She said keeping schools open is essential, but that aggressive contact tracing is no longer happening at schools.
"I don't think we are really trying to stop the spread [of disease] in primary schools... it's not possible to do that within an unventilated classroom with 30 kids not wearing masks".
Dr Ní Cheallaigh said that while vaccines are not yet being administered to those aged under 12, mitigating the risk of infection needs to be considered in primary schools, and expressed concern over the potential impact of long Covid in children.
Meanwhile in Northern Ireland, a further 1,031 confirmed cases have been recorded, as well as six deaths.
