It comes as two computer coding errors left some 6,500 students with at least one grade lower than they should have received last month, and political rivals have now said they believe the Government should have disclosed the flaw sooner.
Labour Education spokesperson Aodhán Ó Ríordáin said he is calling for an independent, non-statutory inquiry into the 2020 Leaving Cert.
"Not only would it exam the process itself but also the decision making, and the handling of the issue by the Department, the Ministers, and the Government.
"Such an inquiry should be headed by an independent figure, either a retired Judge or Senior Counsel, or an expert in the field of education or public administration. It should report as quickly as possible with a deadline of the end of the year."
Serious situation
He said that what is required from the investigation is information on who knew what, an examination of the processes, when decisions were made, why mistakes were not found, and how we ended up in such a serious situation.
He added; "We need to know who was responsible for the mistakes that happened, why they weren't found, who made what decisions over recent months, and an examination of the handling of the issue by the government.
"Critically, there should be recommendations made then on how to ensure such a debacle does not occur again and what changes are needed in advance of the Leaving Cert in 2021 if it is not possible to provide a written exam again."
He said it was "essential" that the Inquiry is independent of government, and that the report the inquiry should then be provided to the Dáil and any findings considered by the Oireachtas Committee on Education.
