The Prince of Wales has said he hopes his mother - Queen Elizabeth - will visit the Republic soon.
Prince Charles was commenting to media in the grounds of Áras an Úachtarain at the start of his two-day visit to Ireland.
Minutes after his arrival he said he looked forward to an historic similar trip which the queen is expected to make soon.
The Prince's jet touched down at mid-morning at Baldonnel from where he was taken to the Áras to meet President McAleese.
Inside the residence the prince met Mrs McAleese on a formal basis for the first time and signed the visitors' book. Asked whether the queen would be coming to Ireland next he replied: "We hope so".
Prince Charles had lunch with Mrs McAleese and a number of invited guests, including British ambassador to Ireland Col Harvey; Prof Frank Convery, head of environmental studies in UCD; and chairman of Tourism Ireland Mr Barry Murphy.
Prince Charles then visited Merchant's Quay Ireland, a homeless and drugs service provider, in Dublin's city centre.
Afterwards, the Taoiseach welcomed Prince Charles at Government Buildings and accompanied him to the Millennium Wing of the National Gallery.
Prince Charles also visited the Abbeyfield Home for the Elderly in Monkstown and the Angel's Quest Respite Home in Glenageary.
The Prince praised those behind the project and outlined his hope that more like it would spring up in Ireland.
"I know what an enormous difference is made to parents of children who are able to leave them here in a sense of comfort and belonging and knowledge they will be looked after," he said.
Before unveiling a plaque to mark the centre's opening, he met some of the parents and children who use it.
Afterwards, Prince Charles conducted an Investiture ceremony in Glencairn, where singer Mr Daniel O'Donnell was among those receiving honorary British titles.
The ceremony will be followed by a private dinner which will be attended by the Tánaiste, Ms Mary Harney, and Mr John Bruton TD.
The Prince will leave Baldonnell at mid-day tomorrow. He will visit the Glencree Centre for Reconciliation, Co Wicklow, in the morning.