"Your royal highness, your presence is greatly appreciated by everyone here today and it has added a unique and inspirational dimension," McAleese said to the prince at a ceremony where they both handed out achievement awards to young Irish adults.
Later, the pair dined in Ireland's Department of Foreign Affairs. Prince Philip, who is also known as the duke of Edinburgh, also was scheduled to meet with Prime Minister Bertie Ahern before traveling back to England.
No British monarch has visited the territory of the modern-day Republic of Ireland since 1911, a decade before the island's partition into a British, mostly Protestant north and an independent, predominantly Catholic south. The southern state became a republic and left the British Commonwealth in 1949.
Since being elected Ireland's symbolic head of state in 1997, McAleese — a Belfast-born Catholic — has regularly expressed her desire to host a visit by Queen Elizabeth II. The two have met four times: Twice in England, once at a World War I commemoration in Belgium, and most recently in Northern Ireland in December.
Politicians from all parties except the IRA-linked Sinn Fein said they would welcome a royal visit to Dublin.
"Hopefully the visit of Prince Philip is a precursor to a visit by Queen Elizabeth at a later stage," said John Gormley, foreign affairs spokesman for the opposition Green Party.
The queen has avoided traveling to the Irish Republic, in part, because of security fears following the IRA assassination of Lord Louis Mountbatten, one of Prince Philip's uncles, in August 1979. Mountbatten, his daughter-in-law and two teenage boys were killed when the IRA blew up his private boat near his castle in County Sligo, western Ireland.
However, both Prince Philip and their eldest son, Prince Charles, have made several successful visits to the Irish Republic over the past decade following the IRA's 1994 cease-fire. Last year, the IRA pledged its truce would be permanent — ending a campaign that left nearly 1,800 dead and thousands more injured — and handed over its weapons stockpiles to disarmament chiefs.