A special Cabinet meeting is to be held tomorrow morning to consider the Protection of Life during Pregnancy Bill 2013, after ministers did not reach the item on today's Cabinet agenda.
A Government spokesperson said it was decided to hold the extra meeting rather than rushing the discussion today.
Meanwhile, the country's Catholic bishops have said that every Irish citizen should be deeply concerned about the Government's planned abortion legislation.
In a statement issued from their summer meeting at Maynooth, the bishops repeated that no individual and no State had the right to undermine the right to life.
It said the planned legislation will, for the first time in Ireland, permit the deliberate and intentional killing of an unborn child.
Archbishop of Armagh Eamon Martin said people are being misled by spin around the legislation, which is due to be enacted before the Dáil summer recess.
Speaking on RTÉ's News At One, Archbishop Martin said legalising the direction and intentional destruction of an unborn baby could never be described in the way the legislation is titled.
The archbishop said the proposed legislation would fundamentally change the culture of medical practice in Ireland because the legislation permitted the deliberate and intentional killing of the unborn child.
On suicidal ideation in pregnant women, Archbishop Martin said the "clear psychiatric evidence" was showing that abortion was not an appropriate response.
He said that better clarity could be found around enhanced medical guidelines that do not envisage killing the unborn.
He accepted that doctors and nurses needed more guidance.
A spokesperson for the Labour Party in Government has said it is "regrettable" that the statement by the Catholic Bishops would suggest that the legislation would "open the floodgates to abortion when the opposite is the case".
The spokesperson said that the Bishops were of course entitled to their view.
A spokesperson for the Taoiseach said Mr Kenny had made his position very clear on this subject, and repeated that there will be no free vote on the legislation.
Meanwhile, it has emerged that the final version of the draft Protection of Life in Pregnancy Bill may not be finalised until tomorrow morning.
The Cabinet is due to meet at 8am to discuss it, and it is anticipated that if approved it will be published tomorrow.
Political agreement on the contents was reached between Health Minister James Reilly and junior minister Alex White for Labour yesterday, officials are continuing work on the actual drafting.
The Government spokesperson said the Cabinet ran out of time to discuss the Bill this morning, but it appears the final legislation wasn't ready in any case.