Thirteen human rights and immigrant organisations have written to the Minister for Justice urging him not to deport up to 11,000 Irish-born children and their families.
The appeal to Mr McDowell comes as the Department begins issuing deportation orders against the non-EU parents of Irish-born children. Some 1,100 letters of intention to deport have been issued since July "as part of an ongoing process", according to the Department.
The move to begin the process of deportations comes after a Supreme Court judgment in January that non-EU immigrants could no longer seek residency here on the basis of having an Irish-born child.
Recipients are being given 15 days to make representations as to why they should not be deported and are being offered no legal guidance in preparing their submissions.
The Department has been issuing deportation orders since receiving and rejecting representations. A number of deportations have already been carried out. Groups working with immigrants say there is no way of knowing what proportion of representation will result in deportation orders.
In their letter the groups - which include the Immigrant Council of Ireland, the National Women's Council, the Irish Council for Civil Liberties and the Children's Rights Alliance - call on the Minister to "regularise the situation of the families of Irish-citizen children who have lawfully applied for residency in Ireland" before the Supreme Court judgment.
They say the families were advised "often by Government officials as well as lawyers and legitimately expected that, on the policy at that time, they would be able to remain and raise their Irish child in Ireland".
The "sudden change" in policy was placing extraordinary uncertainty on those families. The most humane and just decision the Department could reach, the groups say, would be to allow the families to remain in Ireland.