The Taoiseach also said it is now becoming clear that mediation is "not the holy grail or panacea that we thought it was a few months ago."
Leo Varadkar reiterated that he regrets comments he made in May that all cases in the CervicalCheck controversy would not have to go to court.
He said: "I regret that any of this ever happened and as I said many times I feel very sorry for the women who have been affected."
He added: "I have apologised on behalf of the State for the fact the audit was done the way it was done.
"Women weren't told about it and all of those things were wrong. I have said, and this remains our position, we will endeavour to settle these cases by mediation so that women don't have to take the stand in court."
Earlier Fianna Fáil TD Timmy Dooley criticised the Taoiseach for giving the commitment in May that no woman caught up in the controversy would have to go to court.
Mr Varadkar stressed again that mediation is being offered in every case and two cases have been settled this way.
He said: "It is happening again or is about to happen again in the case that is currently before the courts.
"But I do of course regret not being clearer in acknowledging that mediation may not be successful in every situation and that people have the right to decide to take their action to court if they feel that is in their interests. Perhaps I should have been clearer at the time."
The Taoiseach acknowledged "one thing that is becoming apparent to me from the last couple of days is that perhaps mediation is not the holy grail or panacea that we thought it was a few months ago.
"I certainly had much more confidence that we could settle all case through mediation thus avoiding a court trial but it has become evident to me that may not be the case so we need to explore other mechanisms, other alternatives to going through the court process.
"We have had other mechanism, redress schemes for example for similar health scandals in the past. Solutions that I want to find and I'll do my best to find them."
At present a Limerick woman, Ruth Morrissey, is suing the Health Service Executive and two laboratories over the incorrect reporting of two smear tests. That case has been adjourned until September.
Deputy Dooley said the Taoiseach was "in a political corner" so he led people to "believe he was going to do something that he could not do. And in my view, he knew he couldn't do it. He was perhaps hoping for the best. And if he did not know, he certainly should not have known."
He added: "He has foisted an appalling burden on these people who have suffered so much. For political expediency he used language and gave commitments that he was not in a position to do."
Taoiseach 'open to idea' of public CervicalCheck inquiry
The Taoiseach has also said that he his "open to the idea" of the Commission of Investigation into the CervicalCheck controversy being held in public.
He was responding to questions from journalists this afternoon following demands from Stephen Teap and Vicky Phelan earlier in the week for a public inquiry.
Sinn Féin leader Mary Lou McDonald reiterated these claims earlier today.
Mr Varadker was asked if he would support the calls from Ms Phelan, who was diagnosed with terminal cancer last year, and Mr Teap, who lost his wife Irene to cervical cancer.
Ahead of tomorrow's meeting with @PhelanVicky Taoiseach @campaignforleo has said he his open to the idea of the Commission of Investigation into the CervicalCheck scandal being held in public. pic.twitter.com/BHW2e4T2Ie
— Conor McMorrow (@ConorMcMorrow) July 31, 2018
He said he is "very keen" to have the commission up and running. He is meeting Ms Phelan tomorrow and he is aware that one of the issues she wants to discuss with him is how that inquiry will operate.
He said the Government set up the Scally Review to get as many answers to questions as possible and he understands it will be completed by the end of August or early September.
After that, the Government will proceed to establish a Commission of Inquiry.
He said: "I am fully open to the idea of being it held in public but it is important that people understand what the consequences of that will be."
"There will be some people who will prefer to give their evidence in private and maybe do not want to appear in public," he added.
Mr Varadkar also said: "As is the case with any public inquiry it will inevitably involve people seeking legal representation and counsel, the costs associated with that and it could take a long time.
"I don't want to get into a situation where we are promising a quick open public inquiry that answers all the questions then that not happening so it is important that we all understand it will take time and involve a lot of costs. But I am absolutely open to it as a suggestion."
Taoiseach comments on medical negligence payouts
Mr Varadkar was also asked today if he agrees that all of the women affect by the controversy should be getting payouts for medical negligence.
He replied: "The 221 women and their families who are the centre of the CervicalCheck controversy, I think all of them will deserve financial compensation, if only because of what was done to them, the fact that an audit was carried out, an audit found that they had previous false negative tests and that they weren't told about that.
He added: "So I think there's going to have to be some form of financial compensation for them, all 221."
Asked if there are ever consequences for medical staff who are responsible for failings in the health service, he said: "The Medical Council has the role of assessing the performance of doctors, doctors who have may fallen below the standard of clinical performance and there is a number of sanctions that the Medical Council can impose on doctors, ranging from admonishment to being struck off. And people do get struck off and that's done by the Medical Council."
He said: "For nurses it's done through the Nursing and Midwifery Board of Ireland. So I know people may feel perhaps that it should happen more frequently than it does, but these are independent bodies and are set up to make these adjudications themselves, and anyone can make a complaint to those bodies if they feel that they have been badly treated or let down by an individual healthcare professional."
