The Queen opened her speech at Dublin Castle - the seat of British power in Ireland until Partition in 1921 - by addressing guests of the state dinner held in her honour in Irish.
"A hUachtarain agus a chairde" ('President and friends'), she said to the amazement of President Mary McAleese.
On the second day of her trip to the Republic of Ireland, she paid tribute to victims of the Troubles in a powerful and highly-anticipated address.
"To all those who have suffered as a consequence of our troubled past I extend my sincere thoughts and deep sympathy", she said.
"With the benefit of historical hindsight we can all see things which we would wish had been done differently or not at all."
The Queen also praised the strong bond that has now been forged between the two governments.
"That transformation is also evident in the establishment of a successful power-sharing executive in Northern Ireland," she said.
"A knot of history that was painstakingly loosened by the British and Irish Governments together with the strength, vision and determination of the political parties in Northern Ireland."
Standing ovation for the Queen after her speech. A papal visit to Northern Ireland in June 2012 will probably be the next stage in this process.
UTV's Political Editor Ken Reid
The Queen highlighted the legacy of the Good Friday Agreement, praising the work of Northern Ireland's peacemakers.
"Taken together, their work not only serves as the basis for reconciliation between our peoples and communities, but it gives hope to other peacemakers across the world that through sustained effort, peace can and will prevail", she said.
"The lessons from the peace process are clear - whatever life throws at us, our individual responses will be all the stronger for working together and sharing the load."
The Queen referred to the economic challenges currently faced by the Republic of Ireland, but said examining previous problems could provide solutions.
Speaking moments earlier, President McAleese said she was proud of the "peacemakers" who helped to bring about power-sharing in Northern Ireland.
Mrs McAleese said although the path to peace has been "cruelly slow and arduous" it has "yielded huge dividends".
The Irish President said those who want to move forward from violence must be encouraged.
"I am particularly proud of this island's peacemakers who having experienced first-hand the appalling toxic harvest of failing to resolve old hatreds and political differences, rejected the perennial culture of conflict and compromised enough to let a new future in", she said.
Earlier on Wednesday, the Queen visited Croke Park, the home of the GAA, and the day before she laid a wreath in the Garden of Remembrance to commemorate fallen Irish republicans.
The moves have been seen as hugely symbolic and historic acts of reconciliation.
Mrs McAleese acknowledged the Queen's support for the peace process.
"Your visit here is an important sign - among a growing number of signs - that we have embarked on the fresh start envisaged in the Good Friday Agreement.
"Your visit is a formal recognition of what has, for many years, been a reality - that Ireland and Britain are neighbours, equals, colleagues and friends."
Prime Minister David Cameron and Taoiseach Enda Kenny were among the 172 guests at the banquet who also included First Minister Peter Robinson and his wife Iris.
Other guests included Ireland rugby captain Brian O'Driscoll and his actress wife Amy Huberman.
Five people were arrested as dissident republicans protested ahead of the banquet.
Police kept protesters away from Dublin Castle where guests included politicians and churchmen on all sides in Northern Ireland and the Republic. The only party not represented was Sinn Féin.
Party president Gerry Adams said the Queen's speech will be "judged by the actions of her government in the time ahead."
"I believe that her expression of sincere sympathy for those who have suffered as a consequence of our troubled past is genuine", he said.
"Many victims of the conflict will expect her government to act on that as quickly as possible and to deal with legacy issues in a forthright manner.
"Queen Elizabeth's acknowledgement that the relationship between Britain and Ireland has not been entirely benign is a gross understatement.
"This will be forgiven if the future policy of her government is about building an entirely new future based on genuine equality, and mutual respect."