Taoiseach Enda Kenny hit back at the Catholic hierarchy's threat of excommunication for TDs who vote for the abortion legislation.
The possibility of pro-life Fine Gael TDs substantially changing the legislation is being ruled out by several senior coalition figures.
In the wake of the church cranking up its opposition to the legislation, Mr Kenny said the Irish government was obliged to bring in the new laws.
"As I explained to the cardinal and members of the church, my book is the Constitution and the Constitution is determined by the people," Mr Kenny said.
"That's the people's book and we live in a republic and I have a duty and responsibility, as head of government, to legislate in respect of what the people's wishes are.
"Those wishes have been determined and set out by the Supreme Court, which determines what the Constitution actually means."
When asked specifically about Cardinal Sean Brady's veiled threat of excommunication for TDs that voted for the legislation, he replied: "Well, I have my own way of speaking to my God and it's not for me to comment on that."
Mr Kenny said he wanted to bring everybody with him on the passing of the legislation, and it was time to bring "clarity and certainty" to the issue.
"It is a matter for Ireland and for its people. We live within the parameters of the Constitution and strictly within the confines of the law, and that's where the heads of the bill are entirely focused -- within the Constitution and within the law.
"There is no change in the abortion legislation as it applies in Ireland. But it is time to bring clarity and certainty to it and I hope that can be achieved now in an even and considered fashion."
Mr Kenny was speaking at Ireland West Airport Knock, where a statue was being unveiled of the legendary founder of the airport, Monsignor James Horan.
His appearance in Knock came just a day after a vigil against the abortion legislation.
Fine Gael TDs opposed to the legislation want to see the law repealed if the number of terminations increases significantly.
Mr Kenny said there would be mandatory, regular monitoring in the "very small number of cases".
Labour junior minister Kathleen Lynch said the legislation was already restrictive and clear in its intent.