Around 120 women affected by the non-disclosure of the CervicalCheck audit have applied for compensation.
That's according to support group 2-2-1 plus, and follows the announcement by the Health Minister Wicklow TD Simon Harris that an ex-gratia sum of 20,000 euro would be available to them.
The bill will set up a tribunal for women to have their cases heard without having to go to court.
It will operate in a similar way to the compensation tribunal that was set up for those affected by hepatitis C.
It will be chaired by Ms Justice Mary Irvine, and will be optional for women affected by Cervical Check and their families.
The women can still go to court if they wish, but it's intended the tribunal will be faster and less adversarial.
It comes after further controversy around Cervical Check as the State Claims Agency is appealing the case of terminally ill Ruth Morrissey.
The state claims it isn't appealing the 2.1 million euro settlement made to Mrs Morrissey and her husband, but a number of significant legal points that could impact future cases.
The government is hopeful the legislation to allow for an adjudicative tribunal can be passed by the summer recess to avoid more women having to go to court.