The group was earlier told the amendment is "unworkable" in 2017
The Oireachtas Committee on the 8th Amendment has voted that the amendment should not be retained in full in the Constitution.
It is the first vote in the committee after weeks of hearings - with 15 members voting Yes, three voting No and two members abstaining.
The more difficult work will now be deciding between six possible options to be put to the people by referendum.
These will range from a simple repeal of the 8th, to repeal and replacing it with a new law.
The Coalition to Repeal the 8th Amendment says the vote is "an important step forward".
Ailbhe Smyth, convenor of the Coalition to Repeal the Eighth Amendment, said: "Tonight's vote follows on from powerful medical evidence at the Oireachtas Committee hearings earlier today and last week.
"The committee has heard from medical and legal experts, who have highlighted how unworkable the Eighth Amendment is and the grave damage it has caused.
"It is time to remove from our Constitution a clause that has caused so much suffering and misery."
Earlier, the committee was told not to underestimate the anger of women who have to travel abroad for an abortion.
The comment came from Dr Peter Boylan, who says the amendment is unworkable in Ireland 2017.
Dr Boylan is the chair of the Institute of Obstetricians and Gynaecologists.
He says doctors are concerned about women's health.
"I wish to suggest that in 2017, the 8th amendment is unworkable.
"When it was enacted 34 years ago, neither the worldwide web nor the abortion pill had been invented.
"The genie is therefore 'out of the bottle' in respect of online access to the abortion pill.
"The grave concern that we doctors have as a consequence of this reality is a potential for harm, caused by the use of unregulated medication".
The committee has met for the first time since two pro-life members threatened to withdraw from it.
Deputy Mattie McGrath and Senator Ronan Mullen called the proceedings 'a sham', but attended Wednesday's session.
The pro-life politicians claim the proceedings are biased in favour of pro-choice witnesses.
Speaking before the meeting, Senator Ronan Mullen said he holds out little hope for the committee.
"We haven't said that we would withdraw from the committee - we are considering our position.
"But frankly we have no hope on the basis of anything that has happened up to now, that the committee is in the slightest bit interested in rectifying the many problems in its biased approach".
Additional reporting: Jack Quann