The Fine Gael Chairman, Charlie Flanagan, has said he hopes the reservations of some TDs and Senators over the draft abortion legislation will be addressed.
More than five hours of discussions took place between the parliamentary party members on the Heads of the Protection of Life during Pregnancy Bill last night.
The Fianna Fáil parliamentary party will meet this afternoon to begin a detailed examination of the Government's proposed legislation.
Last night's lengthy meeting of Fine Gael TDs and Senators was calmer than last week's discussions with Mr Flanagan saying it was a constructive engagement.
The Oireachtas Health Committee will meet in private at 9.30am this morning to agree its programme of hearings on the draft legislation, which its Chairman Jerry Buttimer has said could be concluded by the end of May.