Sinn Féin's Louise O'Reilly has called on the Government to alter its current plan for the CervicalCheck tribunal in order to make it less adversarial.
Speaking in the Dáil, Ms O'Reilly said that the tribunal, which is set to be established next week, is not currently constituted to deliver justice for the women involved.
She said this has caused huge upset for women and their families and it could have been avoided.
At the very least, she said, that the tribunal's establishment on Tuesday should be deferred.
The Tánaiste said the tribunal is being established in good faith.
Leo Varadkar said the Minister for Health will meet the 221+ group in the coming days and listen to their ideas.
But he said some cases will not be clear cut and there was no way of denying scientists and doctors the right to mount a defence.
Earlier, campaigner Vicky Phelan described the plans for a tribunal as not fit for purpose and a "slap in the face" to the women involved.
Ms Phelan said that unless substantive changes are made, members of 221+ Cervical Cancer Patient Support Group will not be encouraged to engage with the tribunal.
She urged Minister for Health Stephen Donnelly to reconsider the plans, as the legal landscape has changed since the 2018 report into the controversy.
Speaking on RTÉ's Morning Ireland, Ms Phelan said it is exactly one year since then taoiseach Leo Varadkar delivered an apology to the women and those affected by the controversy and they felt heard.
Today, she said, they feel anything but heard.
She said the 221+ group met Mr Donnelly and members of his department about seven weeks ago and raised a number of issues and left feeling encouraged that there would be further consultation.
However, she said, they were left "reeling in shock" to receive a letter two days later rejecting all of their concerns and confirming the imminent establishment of the tribunal.
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Ms Phelan said they were led to believe that the needs of their members, and not those of the HSE and the laboratories, would come first in the Government's response and they cannot understand why the minister would not take the opportunity to work with them.
She urged Mr Donnelly to reconsider and listen to the concerns of women and not proceed with the CervicalCheck tribunal in its current format.
Among the main concerns raised by the 221+ group are the adversarial nature of the tribunal involving the labs, failure to make allowance to allow a woman return to the tribunal if she gets a recurrence of cancer and the statute of limitations.
Ms Phelan said she was weary from all the fighting and thought the tribunal would be a good outcome for women and families but "here we are, two years later nowhere near having something that is actually for the women and that has the women at its heart."
Mr Donnelly said he wants to set up "a system that works" for the women affected and will meet them ahead of the establishment of the tribunal next week.
He said the tribunal is being established for nine months and that no one is being compelled to use it.
Speaking on the same programme, Mr Donnelly said it is "impossible" to be "non-adversarial" but the aim is to set up a tribunal that is "as least adversarial as possible".
He said that it is understood by everybody that claims are paid when negligence is established and that means that "if we don't go with a tribunal and end up back in the courts", the women involved can take cases against the State...and to do so negligence has to be established.
He said this means including laboratories in the process so that questions can be asked and people can disagree.
He said that unless this happens in a tribunal, the State would have to take the laboratories to court and "bring the women in [to court] again" which is not what is wanted.
The CervicalCheck controversy first came to light after Ms Phelan, along with her husband Jim Phelan, sued the Health Service Executive and Clinical Pathology Laboratories Inc, Austin, Texas, over a smear test taken under the National Cervical Screening Programme CervicalCheck and analysed in the US laboratory.
She was diagnosed with cancer three years after her smear test results of 2011 were incorrectly reported as clear of abnormalities.
By the time she had another smear test in 2014 she had cervical cancer.
Since then it has emerged than more 200 women with cervical cancer should have received treatment earlier than they did.