The Minister for Justice has claimed that between 40% and 50% of non-EU nationals who give birth in Ireland do so to gain Irish citizenship for their children.
Mr McDowell also told RTÉ News that he accepted that the Masters of Dublin maternity hospitals had not asked him to change the Constitution.
However, he said they had asked him to tighten immigration controls.
Speaking on RTÉ Radio, the Master of the National Maternity Hospital in Holles Street, Dr Declan Keane, said they had not asked Mr McDowell to take action on the issue of non-national pregnant women availing of a citizenship loophole.
His counterpart at the Coombe Hospital, Sean Daly, told RTÉ that this was a resource issue for the hospitals.
According to figures from the three maternity hospitals, the total number of non-EU nationals who booked in late or who arrived without booking at all last year was 548.
Earlier, in the continuing Dáil debate on the citizenship referendum, Opposition speakers questioned the need to hold it in the light of new figures suggesting that so-called ‘citizenship tourism’ may be very low.
A Government backbencher, David Andrews of Fianna Fáil, also questioned the urgency of pressing ahead with a referendum in June.