A three-hour meeting between the Taoiseach and Cardinal Seán Brady has been described by both sides as cordial and constructive.
The abortion debate was one of a wide range of issues discussed during the afternoon encounter.
Afterwards a Church statement indicated that special attention was given to a shared concern about the problem of suicide across the island.
It reported it had been agreed to continue engagement on the issue with a view to enhancing North/South cooperation.
Consideration was given to commissioning research, as well increasing support for clergy, other professionals, and community leaders.
The meeting was part of a little-used structured dialogue between the State and churches, faith communities, and relevant secular bodies.
Today's delegations included four members of Cabinet and four prelates.
Afterwards, Cardinal Brady said that whilst the dialogue process is still in its seminal stage, its operation bodes well for the future of the country and reflects the maturing character of a truly pluralist State.