Ireland last week published a long-awaited bill that lays down new rules on life-saving abortions, as part of legislative changes promised after Indian dentist Savita Halappanavar died following a miscarriage last year.
Savita, 31, was 17 weeks pregnant when she was admitted to University Hospital Galway last year and died of blood poisoning four days after delivering a dead foetus.
Kenny on Sunday evening said he has told Catholic Church's most senior representative in Ireland Cardinal Sean Brady that politicians have a duty and responsibility to legislate for limited abortion.
"Everybody is entitled to their opinion here but as explained to the Cardinal and members of the church my book is the constitution and the constitution is determined by the people. That's the people's book. We live in a Republic and I have a duty and responsibility as head of the government to legislate in respect of what the people's wishes are," Kenny said.
Kenny was speaking at KnockAirport, where he was accompanied by his party and constituency colleague John O'Mahony, who is one of the Fine Gael (Irish political party) backbenchers with strongest concerns about the legislation.
Kenny said the people's wishes had been determined and set out by the supreme court, which determined what the Constitution actually meant. "People have given their views on this already but it's now a process that we've entered into as a legislature and that's our responsibility in this Republic," Kenny said.
"It is time to bring clarity and certainty to it. It is time to recognise that we've gone on now for 30 years without any regulation without any professionalism involved in this area and that's what this is all about," he said.
Asked if he was concerned about Fine Gael backbenchers voting against the legislation in the Dail (lower House), he said: "Well I would hope that we could bring everybody with us on this matter."
"It is a matter for Ireland and its people. We live within the parameters of the constitution and strictly within the confines of the law. That's where the heads of the bill are entirely focused, within the constitution and within the law," Kenny said.
"There is no change on the abortion legislation as applies in Ireland but it is time to bring clarity and certainty to it and I hope that that can be achieved now in an even and a considered fashion," he said.
The Catholic bishops said they were concerned that hospitals could be forced to provide abortion and that there was no room for conscientious objection at an institutional level.
"This would be totally unacceptable and has serious implications for the existing legal and Constitutional arrangements that respect the legitimate autonomy and religious ethos of faith-based institutions," the Catholic bishops said in a statement.
They also denounced the argument that abortion should be legislated for in the case of a pregnant women with suicide ideation.