Thousands of pupils have been unable to return to classrooms after defects were discovered in a number of schools following repair works to a wall at Oxgangs Primary.
Overall 10 primaries, five secondaries and two additional support needs schools have been closed.
It is understood pupils could return to classrooms by next Tuesday, 19 April.
The council's chief executive, Andrew Kerr, said: "We have plans in place to ensure all primary and special school pupils will be back in schools by next week subject to the Council getting access to the closed schools.
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"Our focus is very much on getting our school children back into education as soon as possible. That remains our priority, particularly for those pupils preparing to sit their exams in May."
Each school was built under a two-phase public private partnership contract by a number of contractors including Miller Construction.
Galliford Try acquired the business in 2014 and has said it has a 'contractual responsibility' for four of the seventeen affected schools.
In a statement, the company said: "Galliford Try takes its role as a responsible contractor very seriously and the safety of the pupils and staff is paramount."
The council added a programme of structural surveys arranged by the Edinburgh Schools Partnership will continue this week, with updated information being confirmed as early as possible in respect of each school.
(LM)
