Mary McAleese has said she is "deeply sorry" for the offence her remarks comparing Nazi hatred with Northern Ireland have caused.
Mary McAleese has been criticised by unionists
The Irish president said children were taught to hate Catholics in the same way Nazis despised Jews.
She said she was devastated by the reaction which her remarks generated and acknowledged she had been "clumsy".
Mrs McAleese made the comments before attending ceremonies marking 60 years since Auschwitz was liberated.
President McAleese said the anti-semitism that existed for decades had been built upon by the Nazis.
"They gave to their children an irrational hatred of Jews in the same way that people in Northern Ireland transmitted to their children an irrational hatred, for example, of Catholics, in the same way that people give to their children an outrageous and irrational hatred of those who are of different colour and all of those things," she said.
However, the president clarified her remarks on Friday.
She said she was "personally absolutely devastated" by the furore, that her critics had been "absolutely right" and acknowledged she had been clumsy and had hurt people.
"I was trying to make a point about the job that we in our time have to do, in a sense to vindicate the dreadful, dreadful, awful consequences of Auschwitz, the things that we have to do to prevent sectarianism and racism in our own time," she said.
"I said that people in Northern Ireland who taught their children for example, to hate for example Catholics, and I should have gone on to say, and Protestants, because the truth of the matter is that, of course, sectarianism is a shared problem."
She said some people had accused her of making a connection between Protestantism and Nazism.
"That's a dreadful assertion and indeed if anybody took that from it I should have to say that I would be very, very, very deeply sorry indeed.
"I was trying to make a point and I made it very clumsily indeed. I am the first to put my hands up and say I made it very clumsily indeed."
Ulster Unionist leader David Trimble told BBC News her words had been "remarkably ill-judged".
"It is most unlike her to make a mistake of that nature, a mistake because it trivialises the experience of European Jewry and trivialises the Holocaust and also causes considerable offence in Northern Ireland.
"While no doubt that is true of some people, it is not right to lump together the Protestants of Northern Ireland and accuse them of this and to ignore the fact that a considerable amount of hatred exists within some members of the Catholic community."
The DUP's Ian Paisley Jnr said her original comments had been irrational and insulting.
Responding, Mr Paisley Jnr said: "So much for bridge-building Mary.
"Her comments are completely irrational and are designed to insult the integrity of the Protestant community and damn an entire generation of Protestant people."
SDLP leader Mark Durkan said the Holocaust could teach everyone "lessons about the danger of unchecked prejudice and unchallenged persecution".
At the weekend, Mrs McAleese said she was pleased and relieved that unionist politicians and Church leaders had reacted generously to her apology.
"I'm very pleased and very relieved that it has been very fast, very efficient and I have to say very generous," she said.
The Irish president said she hoped her bridge-building work had not been damaged by the controversy.