The Alliance for a No Vote (ANV) is calling on the Government to legislate for the X case immediately.
Its call follows yesterday’s rejection of the proposed amendment to the Constitution.
The group also said a debate is necessary on the wider issue of abortion in Ireland. The ANV intends to keep the pressure on the Government until legislation is brought in.
Spokesperson for the ANV Ms Cathleen O'Neill said: "The people have given their verdict on the government proposal, and it is a clear mandate to legislate for the X case.
"Politicians, of whatever party, now have no excuse to avoid the issue. They have to bring in laws to vindicate the right to an abortion for suicidal women.
"We also need to move on and address the wider questions. Rape and suicide victims should be allowed the choice of terminating their pregnancies, as should women, such as Deirdre de Barra, carrying foetuses that cannot survive. "Now that the government's referendum has been rejected, the whole issue of abortion in Ireland has to be addressed properly," Ms O'Neill said.
Another spokesperson, Mr Brendan Young told ireland.com: "The Government is using the excuse of drafting the legislation as a reason for delay. We don't accept that. Hiding behind Justin Barrett is just not tenable".