Initial assessments on schools with structural issues will be completed by Tuesday evening, education minister Joe McHugh said.
A total of 42 are being examined and preliminary indications suggest in many cases the structures are sound.
The developer at the centre of the controversy is Western Building Systems.
Mr McHugh said the review was making progress and praised the role played by principals.
He added: "That puts us in a very good position in terms of analysing that data and obviously to continue the communication with the principals and the school communities."
He said communication with school heads had been pro-active in considering potential solutions.
He added: "As of tomorrow evening, parents will be assured that the opening in the walls, the initial assessments are done, and as soon as we get the confirmation through we will do that in as speedy a fashion as possible."
He said it was an evolving situation.
"An engineering team and a department team are working very closely on that and whatever will be needed will be done thoroughly and the solutions already, as we speak here now, are being put in place for the schools that may have to partially close," he added.
On Monday, Mr McHugh said Ardgillan Community College in Balbriggan would open to all students by Monday week.
The minister said good progress has also been made in putting in place interim accommodation solutions for Tyrrelstown ETNS, St Luke's National School and Gaelscoil Eiscir Riada in Lucan.
Contingency planning is continuing in the event that, following the structural assessments, other schools require some classes to be moved off-site.
The Department has received many offers of support and assistance from schools, clubs and community groups of alternative accommodation options.
Western Building Systems is welcoming the ongoing progress in the Department's assessment of the 42 schools identified and that another group of schools examined today passed the assessment.
In a statement it says with half the schools now assessed, the number of temporary closures remains at two, as originally announced by the Department last Tuesday.
The company says it appreciates fully that this is an important matter, particularly for pupils, parents and teachers at the schools involved.
The comapny says it is engaging constructively with the Department and remains available to meet the Education Minister.
- PA
