Mr Kelly said he will seek to make changes to the Civil Liability Act which will make it easier for terminally ill women and their families to access support.
He told the Dáil that he will do it in honour of prominent CervicalCheck campaigner Ruth Morrissey, who died earlier this week.
Mrs Morrissey, who died on Sunday, aged 39, was among hundreds of women affected by the controversy around incorrect smear test results.
Mr Kelly said that as part of her legacy, the Government should also ensure that the CervicalCheck tribunal is not adversarial.
“I know what she wanted is the Civil Liabilities Act to be amended to do as I just said, and as the chief justice outlined himself,” Mr Kelly added.
Taoiseach Micheal Martin said that Minister for Health Stephen Donnelly is appointing a judge and two other independent members to the tribunal, which was scheduled to begin in March, but was postponed because of Covid-19 restrictions.
Mr Martin said the tribunal was the most effective mechanism to enable women involved to resolve these issues without having to go before the courts.
Mr Martin also apologised to Mrs Morrissey and her family on behalf of the state and acknowledged the litany of failures in the cervical screening system.
“Too many women who should be here and enjoying life with their families are gone because of those failings," Mr Martin told the Dáil.
This government, like the previous government, acknowledges the failures that took place with CervicalCheck programme and are profoundly sorry for what was allowed to happen
“Last July the Oireachtas passed legislation to set up to the CervicalCheck tribunal and the statutory tribunal that will deal with the issue of liability in a non-adversarial way.
After his statement in the Dáil, TDs held a minute’s silence for Mrs Morrissey.
