"We hope that with your help, this year will be a year during which our Government will decide against abortion legislation, and instead opt to protect mothers and babies," the group's website for the event says.
And now pro-life Fine Gael Dublin North-East TD Terence Flanagan says he is seriously considering attending the vigil.
It takes place beside Leinster House and has also been backed by the Catholic Church, with Archbishop of Dublin Diarmuid Martin throwing his weight behind it.
The Government has committed itself to introducing legislation and regulations to deal with abortion, and Mr Kenny has said the threat of suicide would be included as grounds for abortion.
But Mr Flanagan said: "I am pro-life. Fine Gael made promises about this at the last election, as did I when people contacted me about it. It will just become another broken promise."
But he says he has to wait and see what exact legislation is brought forward before deciding how he will vote on the issue. Mr Flanagan added he has to be convinced the legislation would not lead to a liberal abortion regime.
Senator Paul Bradford said he was also considering whether to attend the rally.
"If I happen to be in Dublin on Saturday I might go along," he said.
It has also emerged that the Oireachtas Health Committee will not be making any recommendations to Government on how to proceed with legislation and regulations.
Committee chairman Jerry Buttimer said: "We weren't asked for any recommendations and nor will we be giving any."