The Taoiseach has promised that legislation to allow full disclosure in medical cases will be in place before the end of the year if the Dáil agrees.
Micheál Martin said it was important that the legacy of Vicky Phelan was reflected in changes that would lead to a more "respectful" treatment of women.
He was responding to the Sinn Féin leader, who called for legislation to make sure people will be told the truth when something goes wrong in their healthcare.
Mary Lou McDonald said Vicky Phelan took on the State which had failed her so badly and the best way to honour her is to bring the testing of screening samples back to this country.
"Let's get this done for Vicky," she said.
The Taoiseach added that the new National Cervical Screening Laboratory will become fully operational by the end of the year.
Mr Martin said the lab at the Coombe Hospital in Dublin had been completed in October and would be "operational" by end of the year as a "workforce plan" is in place.
He said while the new lab is due to become the main testing site, the HSE has advised that a secondary contractor will be necessary to ensure there is a "robust approach".
Co-leader of the Social Democrats Róisín Shortall told the Dáil that the State owes a debt of gratitude to Ms Phelan.
She said Ms Phelan was concerned that if she stayed quiet then nothing would change - and she was not willing to accept that.
Ms Shortall said the legislation on mandatory disclosure has been "desperately slow" and four years after the debacle, it still hasn't happened..
The Taoiseach said mandatory disclosure was "imperative" and the legislation can be advanced in a "timely manner" if Government and opposition parties can agree on amendments.
Taoiseach Micheál Martin and Tánaiste Leo Varadkar have paid tribute to Vicky Phelan in the Dáil, hailing her as a 'woman of limitless strength' | Read more political coverage: https://t.co/rJqD002JUG pic.twitter.com/uDZroaF32A
— RTÉ News (@rtenews) November 15, 2022
Mr Martin said the system had failed her dismally and she opened the door to the truth for hundreds of other women.
Tánaiste Leo Varadkar said Ms Phelan was a woman of limitless strength, courage and compassion.
She demanded "action, change and accountability", he said.
Green Party Minister Catherine Martin said Ms Phelan had a steadfast determination to seek the truth.
Sinn Féin leader Mary Lou McDonald remembered cervical cancer campaigner Vicky Phelan in the Dáil saying 'Ireland has lost one of its brightest stars in the firmament of noble women' | Read more political coverage: https://t.co/rJqD002JUG pic.twitter.com/zIOCoeUosA
— RTÉ News (@rtenews) November 15, 2022
Labour Party Leader Ivana Bacik said Ms Phelan's actions had changed many things for the better for many people.
"The reforms that Vicky and others prompted must continue," she said.
Ms Phelan was diagnosed with cervical cancer in 2014. In April 2018, she settled a High Court action for €2.5m with Clinical Pathology Labs US, without admission of liability.
She had undergone a smear test in 2011 showing no abnormalities, before her diagnosis three years later. An internal CervicalCheck audit found the original smear check result to be wrong.
Vicky was a warrior, but the 'gentlest of souls'
Stephen Teap, a founding member of the 221+ CervicalCheck Patient Support Group, has described Ms Phelan as a warrior with the "gentlest of souls".
Ms Phelan was also a founding member of the group. Mr Teap said it is very difficult to process that she is gone.
Mr Teap said along the way people got blindsided by Ms Phelan's strength and somehow forgot this day would come.
Speaking on RTÉ's Morning Ireland, he said: "As the shock of yesterday starts to fade away, we're now waking up to the realisation that our friend is no longer at the end of that phone and our friend won't be returning our messages anymore.
"And there's this massive empty space now beside us all - all her friends, all her family, that Vicky's massive, loving courageous, wonderful personality once filled - has left behind and may never be filled again".
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Describing the last time he met Vicky, he said he could see there were changes in her over the past few weeks and months.
"But she was still upbeat when she would take the calls and give you a call. We're going to miss her, everybody is going to miss her an awful lot."
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Mr Teap, whose wife Irene died from cervical cancer aged 35 in 2017, said he first met Ms Phelan after she won her High Court case and they both were asked to go to the Public Accounts Committee over the CervicalCheck controversy.
He said that despite fighting cancer, she "still had the courage to turn against the system and say no, you're not going to silence me, and I will take you on.
"And compassion for others, because what drove her to do all that was knowing that there were so many other people affected - people like my late wife Irene and many others.
"And while there was absolutely nothing for her to gain from doing this act, it was for everyone else".
He said: "She was fierce. Full of passion, full of drive. Vicky would walk into a room, and everybody stood to attention. She had that personality. But she did it with that beautiful personality and that cheeky grin that she has.
"And while she can be very serious when she needs to be, she's got a fantastic and wonderful sense of humour".
She was a warrior, but the gentlest of souls, he said, and was "just an amazing person and I think anybody that's ever sat in a meeting with her would agree with me."
In relation to campaigning, Mr Teap said: "The truth starts with the truth and ends with the truth, and that's everything and the backbone to everything Vicky fought for.
"And of course, this is everything that we will continue to fight for - transparency in the system.
"The right for people to know what it is going on, especially with their bodies. The right for women actually to stand up for themselves, to have that support, to be able to do so. Not to be afraid, and to be given the respect and the space to do so, and be comfortable enough to be in a position to ask the questions."
Mr Teap added that "there's still an awful lot of work to be done today, there is still a shift in that culture and within our healthcare system that needs to be changed and still a minority within the system that will try and prop it up and hold it up.
"But I think with people like Vicky, myself, Lorraine (Walsh), and many others, we are slowly shifting change and we see it ourselves within the system. But unless it comes from the top, from the Government, unless they get going on what they said they would do and stop dragging everything out.
"We will continue this fight for a very long time, for as long as we have to and will do it in Vicky's name for sure.
"She started the process. She's now handed it over to us and there's plenty of us here."
