Taoiseach Leo Varadkar will issue an apology to all women impacted by the CervicalCheck programme failures in the next Dáil term.
Health Minister Simon Harris confirmed the apology after he and the Taoiseach met with members of the 221+ CervicalCheck patient support group.
The group was set up last year after it emerged 221 women with cervical cancer received incorrect smear results.
"I would expect that apology would be forthcoming in the next Dáil term," Minister Harris said.
A meeting took place between the Taoiseach, Minister Harris and 221+ a day after a rapid review found over 4,080 women had delayed HPV test results communicated to them as a result of an IT problem in a US diagnostics lab, which was contracted by the HSE.
Minister Harris said the meeting was very useful but that he did not want to elaborate on the details discussed.
"I don't want to breach the confidence of that meeting," he said.
"It was a really useful opportunity to catch up on a number of important issues in relation to our screening programme and a chance for both the Taoiseach and myself to thank Lorraine (Walsh) and Stephen (Teap) for the work they're doing," he added.
Ms Walsh and Ms Teap are patient representatives of 221+.
Mr Teap's wife, Irene, died from cervical cancer in 2017. The cancer was missed by two smear tests. Had the illness been detected, her life could have been saved.
221+ said the meeting was the start of a "new dialogue" between patient representatives and the HSE, but that apologies are only possible with a full understanding of what one is responsible for.
"Our patient representatives – Lorraine Walsh and Stephen Teap – met privately this morning with An Taoiseach and the Minister for Health to discuss all aspects of the role of the State in the CervicalCheck debacle and in particular the basis for a formal apology to the women and families impacted," said a spokesman for 221+.
A full apology is only possible with a full understanding of what one was and is responsible for.
He also described the issues in the CervicalCheck programme as a "catastrophic system failure".
"Today’s meeting is the beginning of a new dialogue which is now more properly and fully informed in that regard by the work of people like Dr Gabriel Scally and, more recently, Professor Brian MacCraith which uncovered the shortcomings that led to this catastrophic systems failure.
"Our objective for an apology is that it begins a healing process for all those impacted negatively by CervicalCheck. Today’s discussions embraced that principle and were approached in a positive and constructive manner which we hope will now move to a public conclusion in a timely manner," said the spokesman.
New HSE chief executive Paul Reid had issued a public apology to all affected at yesterday's rapid review report launch. Minister Harris thanked Mr Reid for the "leadership shown", describing it as "very significant".