The BBC's Denis Murray: "A state visit to Ireland by the Queen cannot be too far off"

Greeted by Irish President Mary McAleese at her official residence in Dublin's Phoenix Park, the Duke arrived in an RAF helicopter.

Mary McAleese gave the Duke a warm welcome

They later shared a platform at Dublin Castle for the launch of a new cross-border initiative, bringing together the Duke's awards scheme and its Irish counterpart.

Delivering his only remarks there, the Duke said any attempts to break down divisions between people on either side of the border were to be welcomed.

He said: "I welcome this particular event enormously.

"It will be ridiculous to pretend there haven't been problems between the north and the south and I think that any initiative which can somehow overcome the rather artificial divisions is tremendously good.

"I think if it's going to involve people of the younger age group and I think they can begin to understand each other I think it can only be good for all communities concerned."

Mrs McAleese has recently talked of a new era in relations

Mrs McAleese who earlier described the Duke's visit as a new era for Anglo-Irish relations.

Before leaving for Belfast, the Duke also met Irish Prime Minister Bertie Ahern and other cabinet ministers.

Although the Prince of Wales, the Princess Royal and Prince Edward have all been in Dublin in the past five years, the Duke's trip was seen as the most significant yet.

His visit marked the highest-ranking royal visit since King George V and Queen Mary were there in 1911, 10 years before the country became independent.

It also comes a day before Mrs McAleese and the Queen will inaugurate a memorial in Messine, Belgium, to Irish soldiers who died fighting in British regiments in World War I.

Though government officials warned against the Duke's presence raising immediate expectations, the chances of the Queen visiting the republic soon were seen as realistic in the present circumstances.

Irish officials think the most likely timing for a visit would be in 2000, after all the key provisions of the Northern Ireland agreement are in place.