Minister for Education Norma Foley has said there "may well be" a number of Leaving Cert 2020 students who have to defer as a result of calculated grade errors.
She told RTÉ's Morning Ireland that she did not inform Opposition parties about these errors when first told about them last week, as she wanted exam pupils to have the "fullest of information" about what went wrong.
On the same programme, Sinn Féin's education spokesperson Donnchadh Ó Laoghaire said it is not acceptable that any Leaving Cert student should have to defer due to calculated grade errors.
Ms Foley said it was not known just how many students have been affected by errors in the predicted Leaving Cert grades.
She said a fresh round of offers to students, who were downgraded as a result of errors in their predicted Leaving Cert grades, will be done as speedily as possible.
The minister said she has requested international expert oversight on the process and this is currently being worked through.
Once that analysis is completed, a full file will be made available to the CAO who will then make contact with the Higher Education institutes, who instruct the CAO to make offers to eligible students.
Ms Foley said the Department of Education and the Department of Further and Higher Education will work "hand in hand" to ensure a maximum number of places will be available in this academic year and she is confident that "will be achieved to the absolute limit".
However, she admitted there "may well be" a number of students who have to defer but it was too early to make that call.
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She was made aware of the errors on Wednesday afternoon and the Department of the Taoiseach was informed. Ms Foley discussed it with Higher Education Minister Simon Harris on a later date.
It was only when she had the fullest information, that she made it available - adding that there is more information to come.
She said what happened was unacceptable but action was being taken to rectify the situation. Around 6,500 students received one grade lower than they should have
Ms Foley will discuss the errors discovered in this year's Leaving Certificate calculated grades process in the Dáil this evening.
The full impact of the mistake, and the exact number of students affected, will only be known when a second review of all marks awarded is completed.
Universities have warned that they do not have the capacity to offer places to all students who may receive a new CAO offer on foot of upgraded Leaving Certificate results.
A review will be completed "in coming days" Ms Foley said, and students informed "as soon as possible" after that.
Minister of State at the Department of Higher Education Niall Collins said: "There was no point in the Dáil being informed about the error ... until information was available on what exactly it was, and how many students would be affected."
Speaking on RTÉ's Today with Claire Byrne, Mr Collins said what is important in discussion of the matter is ensuring that "students who have been discommoded will be given a proper offer by the CAO system."
The Minister for Higher Education, Simon Harris has said it will be "more difficult" to create additional third level places for students affected by the error in the Leaving Cert's Calculated Grade system.
Minister Harris said he "arrived at a guestimate of an extra 1,000 places being required, based on the estimate that about 6,000 students are affected."
He agreed that finding these extra places will be difficult but he said his department "will meet the challenge head on."
However, the Irish Universities Association has warned of challenges ahead in providing extra places.
It said there is simply no more space on some courses.
During questions in the Dáil, the Green Party leader and Minister for Climate Action and Transport Eamon Ryan had to defend the Government's approach to the Leaving Cert coding issue.
Labour leader Alan Kelly said of the four layers set up by the Government to ensure calculated grades were going to be checked properly, it did not work and he asked whether it was too late on 24 August to change the model of the system.
Mr Ryan said the predicted results were very close and all the analysis that was done concluded that was what to be expected; the coding error was not seen at that stage back in August.
Sinn Féin TD Ruairí Ó Murchú asked if it is guaranteed that students will get the place in third level they want.
Fianna Fáil TD Jennifer Murnane O'Connor asked about the preparations for next year's Leaving Cert.
Minister Ryan said the Government has committed to keeping schools open and that therefore there will be Leaving Cert exams next June.
He said we will not know the numbers until the code issue is investigated fully.
Reporting Emma O Kelly, Paul Cunningham