Mr Kenny insisted there will be a full discussion on Government plans to introduce a combination of legislation and regulation to legalise the procedure as a last resort when a pregnant woman's life is at risk.
"We will have the fullest discussion about all of this and deal with it comprehensively and sensitively," Mr Kenny said.
"And far from this being any culture of death, it will be a culture of life, about the protection of the lives of women and full respect for the life of the unborn."
The Taoiseach dismissed criticism from the four Catholic Archbishops, who warned the legislation would lead to the intentional killing of unborn children.
Mr Kenny insisted he would not allow a regime of abortion on demand.
He added that he was willing to discuss the planned legislation with the Catholic church during a meeting in January.
Bishop of Kilmore Leo O'Reilly and Bishop of Cork and Ross John Buckley echoed the criticism of Archbishops Diarmuid Martin, Michael Neary and Dermot Clifford, and Cardinal Sean Brady.
Bishop O'Reilly warned the legislation, to be introduced next year, would result in the most liberal kind of abortion. He said the planned reforms would bring about irrevocable change and would lead to what Pope John Paul II called a "culture of death".
Meanwhile, Bishop Buckley described abortion as the most serious threat to human rights.
"It is ironic that the most recent referendum, endorsed by all parties, referred to the rights of children," he said in a statement.
"It now seems that the unborn child can be deprived of the most fundamental right of all, the right to life."
They both supported calls from the archbishops for TDs to be given a free vote on the proposed legislation.
The legislation will be drafted in accordance with the 20-year-old Supreme Court ruling on the X case, which allows for abortion when a woman's life is in danger - including the threat of suicide.
The health committee will hold discussions in January, before draft legislation is published and a full debate held.
The Government followed recommendations in an expert group report published last month - to introduce a combination of legislation and regulations.
The report was compiled to set out options on how to respond to a European Court of Human Rights (ECHR) ruling on the so-called ABC case, which found the state violated the rights of a woman in remission from cancer who was forced to travel abroad to terminate her pregnancy.
Its publication coincided with the tragic death of pregnant Indian woman Savita Halappanavar, 31, who miscarried 17 weeks into her pregnancy.
She died at Galway University Hospital on October 28 after contracting septicaemia. Her husband Praveen Halappanavar claimed she had been denied an abortion.
He refused to co-operate with a Health Service Executive clinical review and an investigation by the Health Information and Quality Authority (Hiqa), and has demanded a full, public inquiry into his wife's death.
Meanwhile, independent health watchdog Hiqa yesterday confirmed the names of members on its inquiry team, which will include four consultants from outside Ireland.
Health Minister Dr James Reilly approved the review team and one other member has to be finalised.