The apology from the President, Mrs McAleese, was welcomed and accepted by unionists, the Orange Order and the Church of Ireland last night.
The Orange Order had cancelled a meeting with the President scheduled for March in protest. However, a spokesman said last night: "The Orange Order is obviously delighted she has apologies for her deeply unfortunate remarks made on Thursday."
He added: "The volume of calls Schomberg House [Orange Order headquarters] had today was just extraordinary - I have never seen such reaction in five years."
There was no rush to review the decision made by the order yesterday to cancel the meeting in Dublin to deal with matters relating to the order in the Republic. It is understood that while the order at official level took a deeply critical position on the President's remarks, some members felt the meeting should go ahead.
The former Church of Ireland Archdeacon of Dublin, the Rev Gordon Linney, welcomed the apology and called for the matter to be left behind. "I think the President's latest remarks are indeed helpful and characteristically gracious," he said.
"I think we should thank her for moving the situation forward. People on all sides should accept that the matter has been dealt with and move on," he added.
Unionists from many parties approved of her apology. Mr Michael McGimpsey, a former UUP minister in the Executive, said: "This puts the matter to rest - the sooner we forget about it and get on with what needs to be done the better." He added: "I think it took some courage to make her apology. Least said, soonest mended."
Ms Arlene Foster, a DUP Assembly member for Fermanagh-South Tyrone, also welcomed the apology. "I'm happy she has apologised," she said. "She's a very intelligent woman and she shouldn't have made those remarks in the first place. She hurt a lot of ordinary Protestants, myself included. I was hurt and I was angry."
Ms Foster, who left the Ulster Unionists for the DUP along with Mr Jeffrey Donaldson 12 months ago, said she did not think the damage caused would be repaired quickly. "I don't think it will be put behind us easily," she said, adding that ground could be made up but it "will need a lot of hard work".
Mr David Ervine, the Progressive Unionist Party leader, doubted that the hurt felt by many unionists would be healed easily. "The damage is massive and the questions are massive," he said.
The Alliance leader, Mr David Ford, said: "The President's fulsome apology clearly demonstrates that she recognises the hurt caused by her careless language. I don't think that anyone who knows the work she has done could have possibly believed some of the interpretations placed on those words and her apology is clear and unambiguous."
The SDLP leader, Mr Mark Durkan, who defended the President robustly yesterday, welcomed her statement.