Mary McAleese is at the centre of a row after claiming Northern Ireland children were taught to hate Catholics in the same way Nazis despised Jews.
Mary McAleese has been criticised by unionists
The Irish president made the comments on RTE radio before attending ceremonies marking the 60th anniversary of the Auschwitz liberation.
The DUP's Ian Paisley Jnr said her comments were irrational and insulting.
The president's spokesperson said her comments were "never intended to single out" Protestants in Northern Ireland.
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.
Mrs McAleese joined survivors and over 40 heads of state for memorial ceremonies in southern Poland on Thursday.
She made the comments in an interview for RTE's Morning Ireland programme.
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.
"Her mask as being a healer of divided peoples has slipped. She is spewing out hatred of the Protestant community, whilst accusing those same people of hating Catholics."
Ulster Unionist assembly member Michael McGimpsey said the comments would outrage people on both sides of the border.
"On the one hand she has shown a clear lack of understanding and sympathy for the Jewish experience under the Nazis," he said.
"To compare the Holocaust, where six million Jews were exterminated, with Northern Ireland shows a total lack of understanding and sympathy."
The former Church of Ireland Archdeacon of Dublin, Gordon Linney, also criticised her comments.
"Frankly, I was shocked and saddened because... of her choice of words," he said.
"If she'd made a political statement that would be for others to discuss, but the fact that she used the word Catholic suggests that people on the other side were Protestant."
Mark Durkan said the president had a "record of bridge building"
However, President McAleese's remarks have been defended by senior Catholic clergyman, Monsignor Denis Faul.
He said she was just giving an example of bigotry adding: "She could have just as easily given an example of political bigotry from the Catholics."
SDLP leader Mark Durkan said the Holocaust could teach everyone "lessons about the danger of unchecked prejudice and unchallenged persecution".
"The Holocaust memorial event in the north has always referred to the lessons for our own society, which has its own prejudices around difference," he said.
"We believe that it was this that the president was saying, as she will be able to show from her own record of bridge-building."
On Friday, a spokesperson for the president said: "President McAleese was responding to a question about intolerance and where that leads.
"She spoke about how great acts of human cruelty have grown from hatred and intolerance and how these sentiments can impact negatively on our children and have massive implications for the future."
The spokesperson also said that her presidency "has been devoted to building bridges between people across Ireland and beyond".
Meanwhile, the Orange Order has cancelled a meeting with Mrs McAleese.
The Grand Lodge of Ireland said it would not take up her invitation to come to Dublin in March, to discuss the concerns of Orangemen in the Republic.
The Irish Labour Party's Ruari Quinn has also said Mrs McAleese should clarify her remarks.