The deputy leader of the Labour Party, Alan Kelly, says he does not believe the current Government will examine the issue of the 8th Amendment to the Constitution.
Mr Kelly's comments come after it emerged that a clinically dead woman, who is 17 weeks pregnant, is being kept on life support because the Constitution affords an equal right to life of the unborn.
The woman's parents, who are her next of kin, may go to the High Court as it is their wish for the life support machine to be turned off.
Minister Kelly says this is a "very difficult and sad case" and "there is no right or wrong answer", but he does not believe the Coalition will look at this issue in the Constitution.
He said: "The issue we are talking about today in relation to the unfortunate woman who is in that circumstance just shows we need to think a lot more about this issue and possibly make further progress into how, as a country, we deal with circumstances like this.
"But I can't foresee that issue being progressed in the lifetime of this Government at the moment anyway."