An estimated 2,000 more school students have been told today to limit their movements, after more than 100 more schools contacted the Health Service Executive over cases of Covid-19 among pupils.
Around 1,500 schools now have pupils forced to stay at home because they have been deemed close contacts.
This includes 580 secondary schools and more than 900 primary schools, according to the HSE's National lead for Testing and Tracing, Niamh O'Beirne.
It brings the estimated number of children affected to 16,000.
Ms O'Beirne said an estimated 150 to 200 more schools were contacting the HSE daily to look for contact tracing to be done, and that on average, every case of Covid-19 among children was yielding 15 close contacts.
The HSE today committed to boosting resources to support schools, after school principals said they were not receiving the support their communities needed in order to ensure that contact tracing was done quickly.
Earlier, HSE Chief Clinical Officer Dr Colm Henry said that at this point in time, they are maintaining the public health advice that children who are close contacts of a confirmed Covid-19 case should stay away from school because of the large number of cases that have been identified.
Speaking on RTÉ's News at One, Dr Henry said last week over 2,000 cases were identified in children under 14 years of age, which "all result in a number of close contacts being identified who are asymptomatic".
He said they are sticking to that policy now, to ensure they break the chains of transmission of the virus, but there is a realisation that the harm resulting from that is greatly reduced because of the impact of the vaccination programme.
He said more HSE resources are being put in place to provide telephone helpline support to schools who need it, and from today, these extra resources will focus on public health departments in the east of the country, where there is a backlog of calls due to school principals.
He said the public health teams have been under pressure in the past week or two, following the return to schools.
The Health Service Executive met the teachers' unions today, he added, and they were given "a balanced view" of the increased number of cases, the testing and the public health response that follows from it.
He said they know that asymptomatic children are "very inefficient transmitters of this disease", that outbreaks in school settings were "not very frequent" and for the most part resulted in small numbers being affected.
He said some of those concerns that they had in the past year that led to these measures are certainly diminished now and while it is important that they stick to the policy, it is also important that they are agile and review it as they go along.
Additional resources for public health teams
Meanwhile, the Minister for Education has said that public health teams will be given additional resources to carry out more Covid-19 tests and advice to schools if necessary but that overall trends showed infections in schools are reducing.
Norma Foley told RTÉ's News at One that 100 additional departmental staff were supporting public health and schools in managing reported cases, but that more resources will be given if the ongoing demand for testing continues.
She said that the 14,000 children currently out of school have not all tested positive and while the schools helpline has seen a high demand in the last number of days, it was working well.
She said: 'It is my view it is working but additional demand is being placed on it."
She said she understands how young people being out of school can discommode them and their families, "but that we must be mindful that we need to remain cautious" as the Covid-19 situation continues.
She said that these 14,000 students are not Covid-positive and the necessity for close contacts to stay out of schools for ten days is being considered.
"We are conscious that public health are reviewing all measures and if it is their view it can be reduced, we will adapt to that also," she added.
Minister Foley said that all accommodations that were required to support school management with the ongoing impact of Covid-19 have been put in place and that school principals should not have to make a public health judgement' in relation to a potential outbreak of the virus.
She said that figures on the rates of infection in schools this week will be available later in the week, but the indication is the trends are positive and infection levels are reducing.
There are 20,000 cases being tested each day, the minister explained.
Principals making judgement calls
Allowing unvaccinated, asymptomatic confirmed close contacts of a Covid-19 case return to the classroom would be a cause for concern, according to the President of the Irish Primary Principals' Network.
Brian O'Doherty said pressures are emerging because, in some cases, principals are being called upon to make judgement calls without the benefit of public health advice when a positive Covid-19 case is identified in a school.
Speaking on RTÉ's Today with Claire Byrne, Mr O'Doherty said that when a Covid-19 case is notified to the school, the school begins a process that involves undertaking a risk assessment to identify close contacts.
When this process works well, he said, it is completed in a couple of hours. However, some current response times are not being measured in hours, but in days, he said.
Mr O'Doherty added that there was a capacity issue and there were similar pinch points last year when there were different waves of Covid-19.
No decision has been made by public health officials on relaxing the rules for children who are identified as a close contact of a confirmed Covid-19 case, to allow those with no symptoms to return to school.
Currently, unvaccinated children who are close contacts must stay out of school and restrict their movements, pending a test on day 0 and again on day 10.
The Department of Health has said the next meeting of the National Public Health Emergency Team will take place on Thursday 16 September.
It is expected to review several matters, including overall Covid-19 trends and a HIQA report on whether masks should be worn by children aged under 13.
Separately, a GP in Co Monaghan has said there has been an increase in children who are testing positive for Covid-19 and who are symptomatic over the last few weeks.
Dr Ilona Duffy said initial Covid-19 cases in schools were picked up in the community, but that a greater spread can be expected in schools as children gather together, particularly among younger groups who do not wear facemasks.
She said there has been an increase in the usual coughs and sniffles and parents are becoming more reluctant to send their children for testing.
Dr Duffy said that she understands the frustration of parents who do not want to have their children tested for Covid-19 when they present with a cough, as they are under increasing pressure with the return to the office and this is creating difficulties.
However, she added, the testing process is phenomenal and the most it will mean is "two days out of school" if the result is negative.
Earlier, Sinn Féin's education spokesperson said a full-time helpline should be set up to help schools cope with cases of Covid-19.
Donnchadh Ó Laoghaire said he has been inundated with calls from principals and school leaders who are frustrated with the Health Service Executive helpline.
Speaking on RTÉ's Morning Ireland, he said that lot of public health work seems to be outsourced to principals who are trying to get their schools up and running at a busy time of year.
Mr Ó Laoghaire also said reports in today's Irish Times that consideration is being given to relaxing isolation rules for children who are considered to be close contacts, but do not have symptoms, suggests to him that the testing and tracing systems appear to be becoming overwhelmed.
Additional reporting Fergal Bowers