The Health Minister Simon Harris has announced a review of the Cervical Check programme following the results of a court case.
Terminally-ill woman Vicky Phelan settled a case on Wednesday, after being wrongly informed she had the all clear and after it taking three years for an audit of her test to be passed on to her.
Cervical Check is writing to doctors to make sure they have told patients the results of the audits of their smear tests.
Meanwhile, the Irish Cancer Society says it understands that at least 14 other women were affected by the review in which Ms Phelan's case was identified.
The society also wants to extend its "sincerest sympathies" to Ms Phelan and her family.
"They have been through a trying and traumatic experience, and we wish her the very best with her continued treatment, and want to offer our support, should she or her family need it.
"A cancer diagnosis is one of the most, if not the most, difficult experiences a person and their family can deal with.
"Doing so at a late stage, in the knowledge that you could have been diagnosed earlier is a harrowing experience, and it is saddening to see cancer patients on the steps of the High Court."
The group adds that it is "fully supportive" of the CervicalCheck programme, "which is truly-life saving."
Minister Harris said the scheme needs to be reviewed.
"We need people to have absolute confidence in our screening programmes - and I have confidence in it: it is a progamme that saves lives.
"But it is a progamme that's 10-years-old this year and I think therefore it is appropriate that we would review it.
"I've asked the director-general of the HSE to review the operation of Cervical Check against best international practice".
Earlier, the Tánaiste Simon Coveney apologised to Ms Phelan and her family.
Speaking in the Dáil, Mr Coveney said: "The tragedy and challenges that Vicky Phelan and her family are facing now have been made all the more difficult because of the failings in terms of the passing on of information.
"For that, as Tánaiste, I want to apologise to her and to her family."
"You need to have confidence"
The Public Accounts Committee (PAC) will be looking into the programme.
Dublin Bay South TD and PAC member Kate O’Connell said the recent case is a worrying development.
Kate O'Connell at the CHQ Building in Dublin in 2016 | Image: RollingNews.ie/Fine Gael
She explained: "I myself this morning booked in an additional check.
"You need to have confidence in this system - it's very important. There's no point in the State rolling out huge money on vaccination against HPV, and then on the other side the last thing is the physical check in this case."
The HSE, meanwhile, has defended the Cervical Check programme.
Dr Jerome Coffey is the director of the HSE’s National Cancer Control Programme with responsibility for the screening services.
He told Newstalk Breakfast earlier: "In the ten years of the screening programme, there's been over three million smears - which is a huge number.
"It's important to say that cervical screening smear tests is the best test, but it's not a perfect test. We know that sensitivity is about 70%, and because of that we repeat smears."
He explained that in certain cases smears are re-reported, and in a 'very small percentage' there is a change in the report - but stressed that international research shows that is not unusual.
He added: "It's vitally important that people continue attending for smears, that they take their advice, and that they have faith in the fact that this is one of the best public health programmes for reducing the risk of cancer anywhere."
Anyone affected by issued raised in this article can contact the Irish Cancer Society on 1800-200-700
Additional reporting: Jack Quann