The President, Mrs Robinson, and the Taoiseach, Mr Bruton, were among those who congratulated Michelle Smith following her Olympic victory.
Mrs Robinson, in a message sent to Ms Smith, said that "on behalf of all Irish people who are celebrating with you tonight, and on my own behalf, I send you warmest congratulations on your marvellous victory.
"Your historic achievement in winning a gold medal on the first day of the centennial Olympics and establishing a new national record has confirmed your position as a superb role model for all young sports people - and in particular for Irish women.
"Your personal determination and tenacity, with your total commitment to swimming, has been justly rewarded. We are all proud of you".
Mr Bruton, in a statement, said: "My warmest congratulations to Michelle Smith for her wonderful achievement in winning a gold medal in the Olympics 400 metre swimming event.
"Her training, dedication and determination have brought her just reward with this great victory. My congratulations, too, to Michelle's family and coach who have supported her in her efforts towards this Olympic achievement".
The Lord Mayor of Dublin, Mr Brendan Lynch, on his own behalf and on behalf of all the people of Dublin, said he wished to convey "heartiest congratulations" to Ms Smith.
"Michelle has achieved what no other Irish woman or no other Irish swimmer has ever achieved before, and we are all very, very proud of her performance. Bravo Michelle."
The Fianna Fail leader, Mr Bertie Ahern, congratulated Ms Smith on her "absolutely tremendous achievement".
The leader of the Progressive Democrats, Ms Mary Harney, said Ms Smith's "gold medal winning performance was a moment to savour and cherish".
