It comes amid warnings from the Chief Medical Officer that the country's contact tracing system cannot keep up with the number of infections.
Cavan, Donegal and Monaghan entered Level 4 last night, while a nationwide ban on household visits also came into force.
Nphet advised the Department of Health on Wednesday that schools are not amplifying the case numbers.
Minister Norma Foley says schools continue to be a safe place to be.
"At all stages, we have in our schools underpinned our activity on the basis of the public health advice available to us.
"The public health advice available to us, and the indeed the national and international experience, tells us that schools are safe places, low-risk environments - and that's largely due to the measures and resources that have been put in place.
"But perhaps more importantly the more generous manner in which they're being implemented in our schools by school communities.
"Equally so, studies were showing that if you were to look at COVID-19 cases in children prior to returning to school and now six weeks into school there is little or no differential there".
"I think there is an acknowledgement in each of the levels one to four that it would be important for our students - and we're aware that when students are out of school how disadvantaged they can be."
She said from level 1 to 4, the public health advice has been that the schools would remain open and she said there has been a discussion between partners in education and society in general that there is a determination to keep schools open.
