Update - 5.58pm: Twenty-two schools remain on schedule to have safety measures in place in time for class tomorrow morning.
One school building will remain closed at phase 1 of Ardgillan Community Colllege in Dublin and 19 schools have been cleared to open fully.
The Department of Education says school principals are being kept informed of progress and parents will be contacted directly by school authorities about local arrangements.
Meanwhile, the Government still has to establish who is responsible.
Communications Minister Richard Bruton, who was in charge of the education portfolio when the controversy emerged, said the matter may end up in the courts.
He said: "Obviously there are issues here on which legal advice will have to be sought by the Department.
"I'm not going to pre-judge what that legal advice would show, but I think the Department has indicated that already itself."
The Minister for Education Joe McHugh says he will try to recoup as much money "as possible" from any repair work needed after structural faults were found in 23 schools.
It is thought the remedial work at the schools built by Western Building Systems could cost millions of euro.
The safety measures, which will be in place by tomorrow, range from fencing and protective decking being installed to minor repairs.
Western Building Systems says the Department certified its work for completion as being "free from defects".
The company insists it did not take short-cuts and will honour its contracts.