The President, Mrs McAleese, and the Taoiseach, Mr Ahern, have sent their condolences to the British royal family on the death of Princess Margaret who died this morning after suffering a stroke yesterday afternoon. She was 71.
President McAleese said her thoughts and prayers were with Queen Elizabeth and her family.
In a statement released this afternoon, the Taoiseach said "on my own behalf and on the behalf of my cabinet colleagues I wish to convey our deepest condolences to you on the death of her Royal Highness Princess Margaret"
It is understood Princess Margaret's funeral will take place next Friday, the 15th of February at 3pm in St George's Chapel, Windsor.
Princess Margaret's death was announced in a statement released by Buckingham palace this morning. It said "The Queen, with great sadness, has asked for the following announcement to be made immediately. Her beloved sister, Princess Margaret, died peacefully in her sleep this morning at 6.30am in the King Edward VII Hospital."
The statement continued: "Her children, Lord Linley and Lady Sarah Chatto, were at her side.
"She developed cardiac problems during the night and was taken from Kensington Palace to the King Edward VII Hospital at 2.30am.
"Lord Linley and Lady Sarah were with her and the Queen was kept fully informed throughout the night. Queen Elizabeth, the Queen Mother, and other members of the Royal Family are being informed."
Princess Margaret suffered at least two previous strokes in recent years.
She was last seen in public before Christmas at Princess Alice, the Dowager Duchess of Gloucester's 100th birthday party.
Margaret was confined to a wheelchair and wore heavy dark glasses, her sight having been affected by a stroke.
The Queen yesterday left Sandringham, her Norfolk estate, and travelled to Windsor where she remained in touch with developments. The royal death will cast a shadow over the Queen's Golden Jubilee.
A long-time friend of Princess Margaret, the Conservative former Cabinet minister Lord St John of Fawsley, told BBC Radio 4's Today programme: "She was a person of such great vitality that her death comes as a particular blow and loss.
"I have got wonderful memories of her. She was the most beautiful debutante of her generation and she kept that beauty right through her life.
"She was highly intelligent. In many ways, she was one of the most intelligent women, one of the cleverest women, I have ever met, and she never really had an outlet for that intelligence.
"She had a turbulent life, of course, but at the close of her life - in the last decade - she had somehow `come into port'. She was not at all unhappy. She loved her royal duties and she did them tremendously professionally.
"She had great satisfaction in the fact that Sarah and David were doing so well. She got great pleasure from her grandchildren.
"One's heart goes out immediately to Queen Elizabeth, the Queen Mother - it is a terrible burden for her to see a loved daughter die - and then to the Queen, because they were very close.
PA