The controversial procedure involved widening a woman's pelvis during childbirth.
It is estimated up to 1,500 women underwent symphysiotomies between the mid-1940s and mid-1980s.
The proposed legislation will allow women to seek legal redress in court.
The legislation was introduced by Sinn Fein TD Caoimhghín Ó Caoláin, who is the convenor of the cross-party group of TDs working on the issue.
The legislation proposed to set aside the statute of limitations for a year to allow victims to seek redress through the courts.
Symphysiotomy was a procedure carried out on mothers before or after labour.
The surgery increased the size of the pelvic area to allow easier delivery of a baby.
The procedure, sometimes carried out without consent or with no information given about its risks, has since been linked with chronic conditions such as pain, incontinence and mobility problems.
Its use began to decline in the late 1950s as confidence increased in the safety of repeated caesarean sections, but Our Lady of Lourdes Hospital in Drogheda, County Louth, continued with the procedure until 1984.
A cross-party private members bill calling for the lifting of the statute of limitations for  symphysiotomy survivors has passed unopposed in the Irish parliament (Dáil).