The Minister for Health has said he only became aware of the reported technical glitch relating to CervicalCheck last Wednesday.
Simon Harris said it was important that an external, independent review was to be carried out by the Health Service Executive in relation to its own processes.
RTÉ News revealed on Thursday that around 800 women who underwent CervicalCheck screening were not issued with their results due to what the HSE said was an IT issue at a US laboratory.
The tests were carried out between 1 October 2018 and 25 June this year and were mainly repeat tests for human papillomavirus (HPV).
The HSE has said that a small number of tests affected by the issue have also been identified outside of this time period.
The problem arose in one Quest Diagnostics laboratory in Chantilly in Virginia in the US, which the HSE said was quality assured and part of extra Quest Diagnostics capacity secured by CervicalCheck.
Mr Harris said the women affected should receive their results by the middle of this week.
He said that what had happened was "not acceptable" and that women needed to be reassured.
The minister said patient representatives were also made aware of the glitch "on the day the story broke" and added that that was was "highly regrettable".
The minister was speaking at the opening of 29 new beds in a ward at Our Lady of Lourdes Hospital in Drogheda.
HSE Chief Executive Paul Reid said he has asked Professor Brian MacCraith to act as the independent external chairperson for the rapid review into the issue.
He is to report to Paul Reid by 2 August.
It will also look at how the IT problem was escalated by the HSE to the Department of Health.
The review will determine the complete chronology of events, from the time the IT problem first emerged, up to the public reporting of the issues last Thursday, 11 July.
It will also examine how the communication of the results of tests to women was managed.
Prof MacCraith will be supported in his work by the HSE's National Quality Assurance and Verification Team and will have access to any external expert.
Areas to be covered by the review
1 To determine the complete chronology of events from the time the IT issues first emerged up to the public reporting of these issues on 11 July 2019.
2 To establish the agreed process for the communication of results to women and their GPs, how this was planned and managed and how this process worked in practice.
3 To determine the adequacy of the response put in place once these issues emerged and to determine where and what the learning is for the management and communication processes within and from the screening programmes.
4 To determine if the relevant procedures as set out in the HSE's Incident Management Framework and Integrated Risk Management policy were followed and implemented.
5 To examine the appropriateness of the escalation and if, how and when the communication of the incident within the HSE's governance structures and between the HSE and the Department of Health, and the relevant Cervical Check committee structures was managed.
6 To provide a report to the HSE's CEO setting out the facts relating to the incident and to make recommendations for any appropriate further actions and future learning.
The HSE has said it is intended that the report of the review will be published.
However, this afternoon 'Sharon', whose case brought the IT CervicalCheck glitch to light, said she was disappointed that the proposed review will be supported by a team in the HSE.
She told RTÉ News that the terms of reference do not determine the scope of who will be interviewed and that it was unclear if the report in its entirety will be published.