Cardinal Seán Brady, the Primate of All Ireland, said the talks were constructive, while the Government described them as cordial and valuable.
Taoiseach Enda Kenny led the talks at Government Buildings and was joined by Health Minister James Reilly, Children’s Minister Frances Fitzgerald, and Education Minister Ruairi Quinn.
After the talks, Cardinal Brady said the Government had said it needed to address the 1992 X case ruling, where the Supreme Court ruled a suicidal pregnant teenager had the right to an abortion.
“They [the Government] stated their position very clearly that they had to act to remedy a situation that [has existed] for 20 years.
“We kept insisting on our point of view and we hope we gave them food for thought.”
Bishop of Ardagh, Colm O’Reilly, said the dialogue was restrained. “We spelled out our position as being unchangeable because of the fundamental problem we have with taking an innocent human life in any circumstances. The Government is under no illusions about that.”
A government spokesman said Mr Kenny outlined the background to the decision to legislate for abortion and the process involved.
He said the course the Government was taking on legislating had not changed, but described the talks as “cordial, comprehensive, and valuable”.
Both sides also discussed the patronage of schools with Mr Quinn indicating that his objective was to increase the choice of the types of schools for pupils.
Cardinal Brady said the closure of the Irish embassy in the Vatican was also raised, that the Government noted his remarks, and had said the situation may change in the future, depending on the economic circumstances.
The meeting occurred ahead of a vigil and rally planned this weekend by anti and pro-abortion sides.
Pro-life campaigners will gather on Dublin’s Merrion Square at 4.30pm today for a protest, where a number of speeches will be made.
A counter demonstration has been organised for the city centre. Sarah Malone, a counter-demonstration organiser, has said pro-choice campaigners will be silent during their rally as they do not want clashes between both sides.