The Department of Health and the Health Service Executive have said that the gradual phased reopening of schools can proceed as planned.
The next phase of return is next Monday for all primary school children in third to sixth class and fifth years in post-primary schools.
In a statement, the Department of Education said that public health has reviewed the measures put in place to ensure safe operation of schools and is satisfied that these infection prevention and control measures, if rigorously adhered to, will keep the school community safe during this period.
More than 320,000 primary children and Leaving Certificate students returned to their classrooms last Monday, 1 March.
They included more than 260,000 junior primary school children, as well as 60,000 Leaving Certificate students.
Special schools also moved to full capacity at the start of March, having for the previous two weeks welcomed just half of pupils on alternate days.
Primary school children do not have to wear masks but those in second level should, officials have been saying in recent weeks.
However, children in primary school are free to wear masks if they and their parents wish to, the National Public Health Emergency Team has said.
Meanwhile, the chair of NPHET's Irish Epidemiological Modelling Advisory Group said there were "no cases in schools last week, but it's very early days".
Professor Philip Nolan said NPHET "will watch it very carefully", but there are no early signs of an increase in disease in younger people or an increase in transmission among adults or more widely in the population as a consequence of school openings in the last week.
He said that any signs of a wider impact around the mobility of the virus would not be seen until later this week or next week.
Prof Nolan said looking at all of the cases in younger people, the number occurring in schools or childcare outbreaks is a tiny component of the overall level of disease in that cohort.
The Deputy Chief Medical Officer said there is nothing to cause concern about the remainder of primary students returning to schools next week.
Dr Ronan Glynn said that NPHET will be watching outbreaks in schools very closely.
He added: "Things have improved significantly and for the better over the past 2-3 weeks and our hope is that they continue to improve".
