President Mary McAleese was among heads of state who were introduced to the new Pope after his inauguration mass at the Vatican this morning.
The President and Dr McAleese briefly met Pope Benedict, who mentioned a previous visit he had made to Ireland and Maynooth University, describing it as a wonderful university.
He told the President 'I will pray for the people of Ireland and I hope they will pray for me'.
The government has said it intends inviting the new Pontiff to visit Ireland.
Earlier, Pope Benedict urged humanity to re-discover God if it wanted to transform what he called the world's 'deserts' of poverty, pain and deprivation into gardens of peace and progress.
Preaching at his inaugural Mass in St Peter's Square, the new Pontiff called himself 'a weak servant of God' and appealed for prayers to help him in what he called the 'enormous task that truly exceeds human capacity'.
The 500,000 pilgrims who the Vatican estimated were in and around St Peter's Square for the Mass applauded the Homily dozens of times.
He said his programme was not to do his own will, not to pursue his own ideas, but to listen, together with the whole Church, to the word and the will of the Lord.
During a two hour inauguration ceremony, he received the official symbols of the Papacy, the Papal ring and the pallium - a narrow stole of white wool.
In his homily, the Pope gave a special message of welcome to the Jewish people.
Special masses were celebrated throughout the country this morning for the new Pope.
In Newry, the Bishop of Dromore said it would take time for Catholics to get to know Pope Benedict and to transfer to him the affection that was felt for Pope John Paul.
