Queen Elizabeth II has offered her deep sympathy to everyone who has suffered in centuries of conflict between Britain and Ireland.

In an address at a State dinner in Dublin Castle, the Queen spoke of the painful legacy of the past and the need to remember all those whose lives have been affected.

The Queen began her landmark speech, which lasted more than eight minutes, in Irish by addressing ‘Uachtaráin agus a chairde’.

The Queen said it was impossible to ignore the weight of history, as so much of the visit reminds people of the complexity of the history between both countries.

She said we must bow to the past but not be bound by it. She said the relationship had not always been straightforward and that the islands had experiences more than their fair share of hardship, turbulence and loss.

The Queen said the experiences had touched ‘us all’, and added that people could never forgot those who had died or been injured.

She extended her sincere thought and ‘deep sympathy’ to those affected, and she said everyone could look back and see things which could have been done differently, ‘or not at all’.

The Queen said it was difficult to have foreseen a time when she and the Irish President could stand together at the Irish War Memorial in Islandbridge.

She said it was almost exactly 13 years since people voted in favour of the Good Friday Agreement, which paved the way for Northern Ireland to become exciting and inspirational.

The Queen said she applauds all those involved in the peace process - the police, An Garda Síochána and other emergency services.

Queen Elizabeth said the challenges of the past have been replaced with new economic challenges.

The Queen praised Mary McAleese and told the President she had done a great deal to promote understanding and reconciliation.

Speaking before the Queen, President McAleese said the royal State visit was the culmination of the success of the peace process and an acknowledgement that whilst the past cannot be changed, there has been a decision made to change the future.

The Queen received a rapturous applause and a standing ovation and ended her speech with a toast to the President and people of Ireland.

Over 160 guests are attending the dinner, including figures from the world of politics, sport, the arts and religious groups.

British Prime Minister David Cameron is also in attendance.

Security around Dublin Castle is extremely tight tonight; there are road closures across the city and guests were subjected to rigorous security checks.

Historic visit to Croke Park

Earlier, the Queen took a tour of Croke Park, the headquarters of the GAA and site of a massacre by British troops in 1920.

GAA President Christy Cooney, President McAleese and the British Foreign Secretary, William Hague, were also present on the visit.

A visit once thought impossible, today occurred under tight security. Just after 3pm Queen Elizabeth II was driven up Jones Road and walked through the Hogan Stand.

She met with players and other groups associated with the organisation.

The Queen was presented with a leather bound history of the GAA, while the Duke of Edinburgh was given a hurley and sliotar.

Mr Cooney said the Queen's visit would result in a further advancement of the Northern Ireland peace process.

Before the stop at GAA Headquarters, the British monarch attended a ceremony at the Irish War Memorial in Islandbridge.

She honoured Irishmen who died fighting in World War I when she laid a wreath at the Irish War Memorial Gardens.

Her first engagement of the day was a trip to the Guinness Storehouse, where, as expected, she did not drink from the Guinness poured for her.

Prince Phillip asked if the stout was made using water from the Liffey.

Guinness master brewer Fergal Murray told him the water was 'pure and pristine from the hills'.

She then travelled to Government Buildings. At 11.12am, a convoy of cars carrying the Queen and the Duke of Edinburgh drove into Government Buildings and staff who had gathered outside applauded the royal visitor.

She signed the visitors' book, met the Government and viewed two parts of the Waterford Charter Roll, dating from 1372.

Taoiseach Enda Kenny and Queen Elizabeth held a private discussion for several minutes.

Rolling road closures across the city were in force again today as thousands of gardaí continue to police the visit.

The disruptions can be expected up until late tonight due to the State dinner.

Tánaiste and Foreign Affairs Minister Eamon Gilmore has said the visit of the Queen shows both countries are coming to terms with our 'complex history'.

Mr Gilmore said today's visit to Croke Park was not just about history, but also about culture.

The Queen, who stayed at Farmleigh overnight, attended an historic wreath laying ceremony at the Garden of Remembrance yesterday.