In the first address of her visit to the Irish Republic, the Queen has extended her deep sympathy to those who suffered during the troubled past of the two countries.
At a state banquet at Dublin Castle, she spoke of the painful legacy of history, but added that Britain and Ireland are now firm friends and equal partners.
The Queen said that with hindsight ''we can all see things which we would wish had been done differently or not at all''.
She went on to praise the ''lasting rapport'' now between the countries.
She acknowledged though Britain and Ireland now have shared economic and cultural links and have worked hard to achieve a peace settlement in British-ruled Northern Ireland, it was impossible to ignore the weight of history.
Scene of massacre visited
Earlier, the Queen visited Croke Park in Dublin - the scene of a massacre by British troops on 21 November 1920.
The crowd was machine-gunned at a Gaelic football match there in retaliation for the killing of 14 British intelligence officers.
Thirteen spectators and a player were killed on what became known as ''Bloody Sunday''.
Earlier, Irish Foreign Affairs Minister Eamon Gilmore said a British monarch walking on the turf, would be a "hugely symbolic" moment.
The Queen is the first British monarch to visit the country for 100 years.