Irish sources confirmed a trip by the Queen is now increasingly likely after a series of trial visits by junior royals, but declined to predict the date.
Such a tour could help to reinforce the political settlement achieved through the Good Friday Agreement, and foster greater reconciliation with the Unionist community.
The memory of the 1979 murder by the IRA of Lord Mountbatten near his holiday home in County Sligo means any visit will not be authorised until the strength of paramilitary ceasefires has been proven and all security concerns have been resolved.
The question may be discussed today when the Queen and the Irish President, Mary McAleese, together attend the unveiling of a memorial in Belgium to First World War dead from both sides of the Irish border.
The possibility of the monarch going to Ireland was raised informally in recent visits by the former Irish President, Mary Robinson, in 1993 and 1996, but no date was set.
Yesterday's trip was kept brief. Prince Philip was gone by lunchtime, making it one of the shortest royal visits to another country.
In Dublin Castle, the seat of British rule until 1922, he officiated with President McAleese at the announcement of a joint awards scheme.
They confirmed that Ireland will host the Millennium Gold Encounter, an event organised jointly by Gaisce, the President's Award, and the Duke of Edinburgh's Award Scheme in Northern Ireland, in the autumn of next year. Young people from all around the world will attend.
The Duke passed rooms in the castle where republican prisoners had been held before their execution in 1916 at nearby Kilmainhaim Jail.
President McAleese skated graciously over the fact that her compatriots had been tortured to death in the basement by Crown forces, mentioning only the fact that the castle "was the main administrative centre" during British rule.
In his brief address, Prince Philip said "it would be ridiculous to pretend that there had not been problems between North and South" but added of the joint awards scheme that "any initiative which can somehow overcome these rather artificial divisions can only be good".Reuse content