The Protection of Life During Pregnancy Bill has passed the second stage in the Seanad by 42 votes to 14.
It will go to committee stage tomorrow.
Fine Gael Senators Fidelma Healy Eames and Paul Bradford voted against the bill.
Earlier, Ms Eames said it was with "a heavy heart" that she could not support the bill.
Ms Healy Eames said she did not want to lose the Fine Gael party whip, however she said she wanted to exercise her human right to make a conscientious decision.
Speaking during the debate on the bill in the Seanad, she said she had been a committed member of Fine Gael for many years.
She added that it was the party that made "a solemn promise to voters not to legislate for abortion".
It saddened her greatly that Fine Gael had broken the promise, she said.
Fine Gael Senator Paul Bradford said most in Fine Gael did not think they would come to the stage in their political lives that the party would be "bringing abortion legislation" before the Oireachtas.
He said it went against the very fabric of the party and goes against what was said before and during Fine Gael's general election campaign.
Senator Bradford said it was "disturbing" to hear ministers saying it was a commitment in the Programme for Government.
He said political scholars in the near future will examine the make-up of the expert group, the terms of reference and the fact its hands were tied and see that the legislation was a "done political deal".
Meanwhile, Fianna Fáil Senator Terry Leydon said the title of the bill was inaccurate and said it should be titled "Abortion Bill 2013".
He said he would vote no to the "blatant abortion bill", which he said would legalise abortion without regard to the viability of the unborn.
Senator Jillian Van Turnhout raised a number of concerns about the bill.
She said the legislation is silent about the access of medical treatment for girls in State care and requested distinct legislation clarifying consent where a patient is under 16.
Despite reservations, Ms Van Turnhout confirmed she would support the bill.
Fianna Fáil Senator Averil Power said "it's ridiculous" that former minister Lucinda Creighton had to resign from her position over the bill.
Senator Power said no member should be forced to vote against their conscience on such an issue.
Fine Gael Senator Catherine Noone said the anti-abortion cause has been undermined by the actions of some.
She said while public discourse is welcome, some tactics had resulted in some members becoming more resolute in their decision to vote for the legislation.
Fianna Fáil Senator Peter O'Brien recalled campaigns in the 1980s, saying they were "nasty" and he welcomed how the "country has moved on".
Labour Senator Jimmy Harte congratulated the Taoiseach and the Tánaiste for introducing the legislation, claiming that Fianna Fáil was always "looking down the road" at the reaction of the church.
Mr Harte said women had not been respected by the Catholic Church for thousands of years.
He said the 50% of the country who are male should not be talking about this issue, saying it was a matter for women.
Fianna Fáil Senator Paschal Mooney took issue with that comment.
He questioned why men should be "completely ignored", given that they help create the unborn.
Fianna Fáil Senator Denis O'Donovan confirmed that he would not be supporting the bill.
He said his decision came following a meeting with the Master of the Rotunda Hospital, Dr Sam Coulter Smith.
Senator O'Donovan said Dr Coulter Smith gave the view that in a situation where someone is suicidal there is no medical evidence to have a termination for that reason.
The senator said he held the doctor's view in high esteem.
Fine Gael Senator Eamonn Coghlan said he was reluctant to get involved in the debate, but he felt he was damned if he did and damned if he did not.
He spoke of being threatened walking in and out of Leinster House, receiving abusive phone calls at home and at work, and about receiving "warped" emails.
Fine Gael Senator Michael Mullins said he would support the bill because he trusted that women and the medical profession would not abuse the legislation.