The Minister for Justice has ruled out the introduction of a national identity card.
Mr McDowell said such a card, on the continental model, would "irrevocably and irretrievably" alter the relationship between the ordinary person and the police force.
"It would make the police the enemy rather than the friend of the people. There are privacy issues and civil liberties issues to be considered," he added.
He rejected claims that Ireland was a racist society. "In fact, I assert the opposite."
He said Ireland had been confronted with rapid change in circumstances where it was not used to multiculturalism, immigration and the like. "It suddenly found itself sucked into a situation which many of did not anticipate until it was upon us.
"However, looking at the streets throughout the country, the way the immigrant populations have assimilated into our community and the general attitudes in public and private discourse, I believe this country has been remarkably free from racism."
Mr McDowell said there had been isolated attacks with a racist motive, "but people who attacked other people and kicked them on the ground, people who get drunk and use bottles on other people, who carry knives with which they threaten others are not usually the most gentle or discerning elements of our population."
Replying to the debate on the Immigration Bill, the Minister said that even those who were reticent about immigration were, generally, free from racism as their primary motivation.
"We have not had race riots, thank God, and I hope we never will. We have not had groups of youths from a community assembly to threaten or use violence on other groups.
"We have been free of that, so let us keep our comments about ourselves in proportion. We have equality laws which are among the most advanced in the world. Ireland cannot be characterised as a racist society."
He said there was a tendency to ascend moral pulpits, particularly on the racism issue.
"The vast majority of members of this House, and the members of the other House, are all people who see all of the problem in all of its complexity and see the human side to every single aspect of it," he added.
Earlier, Mr Paul Gogarty (Green Party, Dublin Mid West) said Ireland was becoming increasingly racist and this was partially the fault of the Government through its policies of not promoting a more inclusive society and for not having a sensible view on immigration.
"My only inherent prejudice is that I am similar to other Irish people who have racist tendencies, but I try not to have them," he said.
"Even discriminating positively towards a foreign person is a form of inverse racism. The sooner we treat people, no matter where they are from, as people and recognise their rights, the better." The second stage of the Bill was passed by 64 votes to 54.
