It says "that publicity around the case and/or settlement is likely".
He said all patients should be contacted by their hospital today.
An audit found that further action should have been taken in the cases of 208 women diagnosed with cervical cancer whose original smear tests were reviewed.
A review conducted by the HSE confirmed 208 women should have received earlier intervention than they did but only 46 individuals were made aware of this.
In a statement posted to their website, the society began by sharing their sympathies following the announcement that 17 women who had been affected by the smear test controversy have died.
The cause of death of those 17 women is not yet known.
The Director General of the HSE yesterday suggested that women might prefer to ask for a review of their slides, as the issue was with the screening part of the check, rather than the taking of the smear, which is much more invasive.
However, he said he would not have gone on RTÉ News to express a lack of confidence in the management of the service.
Ms Phelan has said she does not believe Mr O'Brien learned about her case last week.More news: IPhone X blamed for Apple's slow growth in smartphone sales
The Minister for Health, Simon Harris, and the Tanaiste, Simon Coveney, have apologised to Ms Phelan and her family. He is expected to discuss this issue with the Taoiseach Leo Varadkar in the coming days.
The inquiry "will look at the laboratory testing, and whether a different form of testing might have reduced the the number of false negatives", he said.
The issue has raised significant concern regarding the screening tests for cervical cancer.
A plan for a Hiqa investigation into the CervicalCheck screening programme was approved by Cabinet this morning on the back of the deepening scandal.
He said it would have full powers to compel witnesses and documents from the HSE and his department.
It will carry out independent clinical reviews of the women affected. It will provide for mandatory open disclosures of serious health incidents.
Vicky Phelan's lawyer, Cian O'Carroll, called the conduct throughout the process appalling and said, "it is particularly disgusting when you learn of the number of people that have died".
It also says no quality issues have arisen with regard to the USA lab examining smear tests.
Every woman who had a smear test and wanted a recheck for reassurance can have it arranged by her GP and paid for by CervicalCheck.