His move came after Junior Minister Lucinda Creighton said she would "struggle" to decide on how to vote on the forthcoming abortion legislation. And Transport Minister Leo Varadkar raised the possibility at the Fine Gael parliamentary party that it might require another referendum.
But Mr Kenny specifically promised there would be strict limits on abortions to save the life of the mother. This was in response to concerns from Fine Gael TDs that legislation would lead to "abortion on demand".
"I think this is a case of being clear about the introduction of rules here that give clarity and legal certainty and restrictions, on the other hand, on what is a very liberal regime without any terms and conditions," he said.
Mr Kenny said the Cabinet would make its decision based on the options in the expert report before the end of the Dail term.
But Ms Creighton showed the level of concern in Fine Gael when she said that any attempt by the Government to impose a "three-line whip" to force TDs to back abortion legislation would not be appropriate.
"I certainly will struggle with it. I can't tell you how I will vote as I don't know what I will be voting on," she said.
Ms Creighton added that she did not accept there was no choice but to legislate.
"There are deep concerns that if we get it wrong, this could lead, for example, to abortion on demand," she told RTE's 'Today with Pat Kenny Show'.
The abortion issue has also caused problems for Sinn Fein. Senior party figures admit they do not even know the rules of how to deal with Meath West TD Peadar Toibin, who did not vote on an abortion bill in the Dail last Wednesday night.
Mr Toibin has said he does not want to legalise abortion in line with the X case.
He admitted: "I have no iota of when the disciplinary action will be taken or what it will be. I expect some disciplinary action and I fully accept that."
Sinn Fein health spokesman Caoimhghin O Caolain said the party would decide what to do with Mr Toibin in "good time".