A Fine Gael MEP has said Ireland has not taken in the number of refugees we should have.
It comes after the deaths of 71 people who were found in the back of a lorry which abandoned on a roadside in Austria.
Four children, including a one year old girl, are among the dead.
Four people have been arrested.
German Chancellor Angela Merkel says some countries, including Ireland, Denmark and the UK, are not taking part in the common European asylum policy.
Fine Gael MEP Brian Hayes says a number of criteria should be taken into account when deciding how many refugees countries accept: "Where is the strength of the country, where is the underlying demographics of the country, is it a young country, an older country, where is economic growth in that counrty.
"How many people have been taken thus far, and I'll be the first one to say in terms of numbers, this has been a historic problem in Ireland, we have not taken the numbers that really we should have taken in the context of other countries."
"Largely because we have a land boarder with the UK and we are outside the Schengen Agreement, which in other words, people have freedom of movement between Britain and Ireland," said Mr Hayes.