The Dáil will debate the report of the Oireachtas Committee on the Eighth Amendment of the Constitution on Wednesday and Thursday.
Meanwhile, the Fine Gael Parliamentary Party chairman has said his party had a "respectful and thoughtful" discussion on the report of the all-party committee.
The report recommended unrestricted terminations up to 12 weeks of pregnancy.
The meeting lasted five hours and around 60 members of the parliamentary party attended, 30-40 of whom addressed the meeting.
Many members said irrespective of how they felt, they had started a process and they should complete it by putting the committee's proposals to the electorate. Senior ministers Charlie Flanagan and Pascal Donohoe were firmly of that view.
A number of party members, including Tánaiste Simon Coveney, said it was important that the draft legislation which would show people what impact the referendum would have if passed should be published in a timely manner.
Martin Heydon said the discussion reflected the fact that the party is a broad church.
Taoiseach Leo Varadkar told the meeting that the report's recommendation were a strong option.
Deputy Heydon was asked what Mr Varadkar meant by this - he said the Taoiseach was referring to the fact that there had been a process and an all-party committee looked at the issue and they would need a good reason to go away from its recommendations.
He also noted that it was a minority Government.
Mr Heydon told the media there had been some moving contributions from TDs who had personal stories.
He also said questions were asked about the legislation that would give effect to the referendum.
As he arrived for the meeting, Minister of State Pat Breen said it was likely that Mr Varadkar would wait until the Cabinet had agreed a position on this issue before the end of the month before outlining his opinion.
Mr Breen said he had concerns about the 12-week recommendation, but would listen closely to today's debate.
Senator Martin Conway said abortion remains an emotive subject but the people should have their say in a referendum.
MEP Mairead McGuinness said many in her party had a nuanced view on this issue and their positions are not yet confirmed.
TD Kate O'Connell said it was important that indicative legislation, that could replace the Eighth Amendment, is published soon.
An independent facilitator, Lucy McCaffrey, attended the meeting.
On RTÉ's Drivetime, Minister for Housing Eoghan Murphy said he hopes that TDs and senators who believe the Eighth Amendment should be repealed will make their views known when when the issue is debated later this week.
He said it was an important issue for Irish society and a sensitive area of life.
On the same programme, Fine Gael Deputy Hildegarde Naughton described the parliamentary party discussions as calm, adding that a variety of views were expressed.
She said she is in favour of abortion up to 12 weeks.
She believes there is an openess from others within the parliamentary party to learn.