Opening a two-day Dail debate on repealing the Eighth Amendment, Mr Harris said: "These are not faceless women".
Mr Martin said he supported the logic and the basic approach proposed by the committee.
More TDs and Senators are giving their opinions on the recommendations.
Women from every county in the Republic of Ireland travelled to the United Kingdom to access an abortion and I think we have to acknowledge them all. He said that 28 women from Offaly made that journey in that time.
SPUC's review of medical literature Abortion and Women's Health identifies social and emotional support as being of "vital importance" in the context of unexpected pregnancy, and lists numerous motives underlying an abortion decision which arise as a result of this support being absent.
"There appears to be no sound basis for pointing to other countries and saying that Ireland will become like them by changing its laws".
"Because it seeks to force women to carry a pregnancy to term when they have been the victim of a rape or incest or when they have received the diagnosis of a fatal foetal abnormality".
He believed "forcing a woman to continue with a pregnancy in the hope that there may be somebody willing to adopt, I find that obscene". It is an issue that troubles most of us as individuals.
Mr Martin told the Dail he was keen to see legal advice being drafted for the Government on whether the Eighth Amendment should be repealed or repealed and replaced.More news: CBB: Is this the HUGE nominations twist?
The debate involved speakers from all parties including committee members.
At the start of a Dail debate that gave TDs the opportunity to state their position on the issue, Mr Harris said that in 2016 3,265 Irish women travelled to the United Kingdom alone to have an abortion.
She accused the church and state of historical collusion on issues like contraception and abortion.
"Their babies were sold like puppies to foreign homes or enslaved in industrial schools, to be preyed upon by those in power-wielding authority".
The Dáil and Seanad are discussing the recommendations of the Oireacthas Committee report on the 8th amendment.
In an impassioned speech in Dáil Éireann on Wednesday, Minister for Health Simon Harris went county-by-county, detailing the 3,625 women who travelled to England in 2016 for an abortion, calling it "a sad reality that we've been exporting this issue for decades".
"We can not allow the baby in the womb to be described as nothing more than a clump of cells - which has happened too much to date".
He added that he was aware that some people believe that legalising abortion will cause women to use "abortion as a contraceptive" which he called "a grotesque and offensive view of women".