Two TDs clashed over immigration during a series of Dáil debates to mark Europe Day.
Fine Gael chairman of the Joint Committee on European Affairs John Deasy said it was "neither surprising nor earth-shattering" that the committee's main finding was that one department and one Minister should be given for immigrant affairs in their entirety.
"The numbers involved are staggering. It is possible that one million immigrants will come to this country over the next 10 years. The social aspect of such arrivals has been stressed repeatedly," said Mr Deasy.
"The members of the joint committee have stressed that if we do not deal with the social issues facing immigrants, we will encounter major problems down the road," he added.
Barry Andrews (FF, Dún Laoghaire) said he disagreed with Mr Deasy, adding that only last week the committee had met with the Bulgarian ambassador.
"She was able to inform us that labour market movements within Bulgaria are completely different to the situation as described by Deputy Deasy. There is very little likelihood of any major rush from Bulgaria. They have had 5 per cent to 6 per cent growth on average over the last three or four years.
"There does not appear to be any question, if immigration from the 10 accession states has been moderate, measured and useful, that opening the borders to Bulgaria and Romania will be a regressive step."
Minister for Enterprise, Trade and Employment Micheal Martin said he agreed with Mr Deasy and Mr Andrews that the Government's decision to grant immediate free access to the labour market for nationals of the new member states from May 2004 was the correct one.
"I do not say there are no issues to be addressed, but we should focus on the fact that we still have significant shortages of people in information and communication technologies, health care, research, development and engineering."
On future accessions to the EU, particularly Romania and Bulgaria, the Government would make a decision after consultation with the social partners, as had been agreed, said Mr Martin.
Fine Gael spokesman Phil Hogan said migrant workers needed considerable assistance in a number of areas, especially in terms of education. "Irish people also need to be educated about the importance of migration."
Ciarán Cuffe (Green Party, Dún Laoghaire) said his party believed a minister of state, based in the Department of the Taoiseach, should be given responsibility for immigration and ethnic affairs.
Labour spokesman Michael D Higgins said the Government should revisit the issue of signing and ratifying the international convention on the protection of the rights of all migrant workers and members of their families.