Initial checks will be finished by the end of the day on 42 schools over structural concerns.
Examinations are being conducted at schools built by Western Building Systems.
Two schools in Dublin were closed over structural concerns last week.
Three schools need internal and external intervention to ensure the re-opening of the ground floor areas - Tyrrelstown Educate Together National School, St Luke's National School, Tyrellstown and Gaelscoil Eiscir Riada, Lucan.
Officials are working to find interim accommodation for any affected classes.
Two other schools - Scoil Chaitlín Maude in Tallaght and Castlemills Education Centre in Balbriggan - have been identified where an intervention is needed in the form of a fence around the building and some protective decking, but the schools are expected to re-open as normal after the mid-term break.
Education Minister Joe McHugh says work continued over the weekend to complete initial assessments of 42 schools.
Education Minister Joe McHugh. Picture by: Artur Widak/SIPA USA/PA Images
He said: "There's been a very intense investigation and work carried out over the weekend, and we will continue to try to get as much information to the principals prior to the children coming back in advance of next Monday.
"Fundamentally the whole way through this process, the safety of the pupils and staff is at the forefront of our minds."
He indicated that initial feedback from the assessments appears to be "positive", but stressed that final analysis has yet to be completed.
Meanwhile, Western Building Systems said that a group of schools examined yesterday passed the assessments - noting that has been the case with most schools so far.
A statement adds that the company is 'engaging constructively' with the Department of Education.