Mr Kenny said he has a "duty and responsibility" to legislate for people's wishes and that it is time to bring clarity to the issue.
He also said he hopes the entire Fine Gael parliamentary party will vote for the planned abortion legislation when it comes before the Dail.
The Church had left the threat of excommunication hanging over the heads of Catholic members of Leinster House who vote for the laws.
When asked about this, Mr Kenny replied: "I have my own way of speaking to my God. It's not for me to comment on that."
The Taoiseach said he explained to Cardinal Sean Brady that: "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."
He said the Supreme Court "determines what the Constitution actually means".
In the 1992 X case, the court allowed a suicidal pregnant teenager to have an abortion.
Mr Kenny said: "It's time to bring clarity and certainty to it. It is time now to recognise that we've gone on for 30 years without any regulation, without any professionalism involved in this area."
His comments came as another minister said that the health minister will have the right to intervene if a hospital carries out an inordinate amount of terminations.
Labour TD Kathleen Lynch said strict reporting mechanisms will be set up to monitor hospitals.
Ms Lynch, a health minister of State, said the laws will be "very restrictive" and any attempt to widen the criteria would have to be put to the people by way of a referendum.
"What is built into the legislation is that there is a reporting mechanism and that's to ensure that mothers are kept safe while in pregnancy.
"If you had a situation where it became quite clear through that reporting mechanism that one particular hospital was carrying out an inordinate amount of terminations, then clearly the minister would have the right to step in and ensure that women's lives are protected."
It has also emerged that Fine Gael has confirmed anti-abortion backbenchers will be able to introduce amendments to proposed legislation.
Fine Gael chairman Charlie Flanagan said: "There will be an opportunity for amendments.
"This isn't just a parliamentary rubber-stamp. I wouldn't like people to think this is a fait accompli because it isn't."
Meanwhile, Fine Gael European Affairs Minister Lucinda Creighton, one of the most prominent opponents of legislating for abortion, said she has no immediate plans to resign.
But she said she still has difficulties on including suicide as a ground for a termination.
Thousands attended Knock shrine in Co Mayo over the weekend when a national prayer vigil for the right to life of mothers and babies was held.
READ ANDREW LYNCH, P14