Pavee Point Traveller and Roma Centre has called on the Minister for Children to establish an independent review of two cases in which children were taken from their families.
The organisation said it was "disturbed that there have been two recent cases of young Roma children being removed from their families as a matter of first resort and not as a matter of last resort".
Pavee Point said it was worried that these types of incidents will "fuel racism against Roma".
Minister for Children Frances Fitzgerald said that, while she could not comment on individual cases of children being taken into State care, the child's best interest is always paramount.
"Child protection is at the centre of any decisions that are taken, where gardaí or social workers act in cases where children are taken into care," Ms Fitzgerald said.
"It's always about child protection and the best interest of the child."
The minister said there are currently 6,000 children in State care in Ireland, a number that has been rising.
"Children coming into care unfortunately is a common occurrence in Ireland at present, but compared to other countries we do not take many children into care," she said.
She encouraged members of the public to remain vigilant and contact the authorities if they have suspicions about the welfare of a child.
"As Minister for Children, I would be encouraging people to report if they are concerned about children," she said.
"We are going to put Children First [national guidance for the protection and welfare of children] on a statutory basis to make sure if there are real concerns about child abuse of child protection that they are reported. It is extremely important that the public are vigilant."
Elsewhere, the Executive Director of the European Roma Rights Centre also expressed concern at the way two cases of children removed from Roma families in Ireland and Greece are being reported.
Dezideriu Gergely said he was worried that a link between the two stories was being made prematurely.
Speaking on RTÉ's Morning Ireland, Mr Gergely said reporting has to be focused on fact and not on assumptions based on the Roma community.
He said there was an emphasis of criminality being put on Roma in Europe, which was unfair.
Mr Gergely said it is important to remember that not all Roma are dark-skinned and many do have pale skin and blonde hair.
He said: "The concern related to these cases is that, one way or another, if these cases are not discussed from all angles possible, there's this, if I can say, trap to fall into, basically labelling the whole community for being responsible for something, which needs to be looked at from an individual point of view and responsibility point of view".