The Irish Immigrant Support Group (NASC) launched its No campaign against the citizenship referendum.
NASC, which takes its name from the Irish word for "link", is a Cork-based organisation which provides a centre where immigrants can meet and puts them in contact with voluntary and statutory services.
It argues that the proposed amendment is "unnecessary".
Ms Gertrude Cotter, co-ordinator of NASC, said yesterday that the Government has failed to allow time for debate.
"What the Government is actually proposing will mean that in future there will be two classes of Irish children: those who are nationals because they are born in Ireland and therefore part of the Irish nation.
"The second are those who are non-nationals and citizens because of who their parents are.
"This completely contradicts the Republic's Proclamation that it would 'cherish all children equally', and the constitutional guarantee of equality," she said.
Ms Cotter dismissed the claim that this is a technical amendment to close a loophole.
"There is no recent 'loophole'. Ireland has had exactly the same basis for citizenship for the last 83 years," she said.
There was no statistical evidence from the Government documenting a substantial number of non-national women arriving in the country in the late stages of pregnancy, Ms Cotter said.
"These late presentations are a fraction of the births to non-nationals lawfully living in Ireland, which means that the Government's argument is that you should deprive 95 per cent of children of their rights to target the parents of 5 per cent of children who you believe to be 'taking advantage', rather than deal with an identifiable issue."
Labour's deputy leader, Ms Liz McManus, yesterday accused the Minister for Justice, Mr McDowell, of overreacting to a preliminary judgment earlier this week by the European Court of Justice which said a Chinese mother and her Irish-born daughter are entitled to live in any EU country on account of the child's Irish citizenship.
Ms Man Levette Chen went to Belfast in 2001 to give birth to a daughter, Catherine, after a lawyer advised her that the child would acquire Irish nationality.
"Free movement of persons within the European Union is still quite severely limited ... If you are not 'economically active', then your rights are curtailed," Ms McManus said.
"There seems to me to be no great likelihood of floodgates being opened by reference to the Chen case," she said.