Pope John Paul II has told the President, Mrs McAleese, Ireland has an "essential role" to play in affirming its Christian identity in an enlarged EU.
The frail pontiff appeared in good form as he welcomed the president to the Vatican and read a brief speech after their 10 minutes of private talks.
"Ireland, with its rich Christian history and its outstanding patrimony of spiritual and cultural values, has an essential role to play in the building of the new Europe and the affirmation of its deepest identity," the Pope said.
The Vatican has been battling for recognition of Europe's Christian roots in the EU constitution, which is being drawn up. However, other interests are deeply opposed to the mention of any religion in the constitution of a political, and arguably secular, entity.
Pope John Paul also expressed "my deep affection for the Irish people" and sent his greetings to them.
He presented the president with a bronze of the Madonna and child as a gift for the Irish people. As her gift, Mrs McAleese gave the Pope a book recounting John Paul's 1979 Irish pilgrimage and a chalice.
The main purpose of her visit is to attend the celebrations for the 375th anniversary of the Pontifical Irish College.
This evening, she will address the collegeconference Faith and Culture: Ireland and Europe, Yesterday and Today. She will also unveil a monument to Irish colleges in Europe.
Tomorrow, Mrs McAleese will meet the Italian president, Mr Carlo Ciampi, before attending an Irish community reception hosted by the Irish Ambassador to the Holy See.
Additional reporting PA