"The Lord is calling me to 'climb the mountain', to devote myself to prayer and meditation," the 85-year-old Pope told the crowd on Sunday as he appeared at the window of his apartment overlooking the square.
"But this does not mean abandoning the Church. If God is asking me to do this, it is so because I can continue to serve the Church with the same dedication and the same love, with which I have done thus far, but in a way that is better suited to my age and my strength," he said.
"Thank you for your affection," the Pope added.
Pope Benedict XVI shocked the world earlier this month with the announcement that he would step down as head of the Catholic Church Feb 28 due to old age and failing health.
"I declare that I renounce the ministry of Bishop of Rome, Successor of Saint Peter, entrusted to me by the Cardinals on 19 April 2005, in such a way, that as from 28 February 2013, at 20:00 hours, the See of Rome, the See of Saint Peter, will be vacant," Vatican Radio quoted the Pope as saying in a declaration.
"After having repeatedly examined my conscience before God, I have come to the certainty that my strengths, due to an advanced age, are no longer suited to an adequate exercise of the Petrine ministry," he said.
"In today's world, in order to govern the bark of Saint Peter and proclaim the Gospel, both strength of mind and body are necessary, strength which in the last few months, has deteriorated in me to the extent that I have had to recognise my incapacity to adequately fulfill the ministry entrusted to me," he added.
"A conclave to elect the new Supreme Pontiff will have to be convoked by those whose competence it is," he said.
Pope Benedict XVI was born Joseph Aloisius Ratzinger in Bavaria, Germany, in 1927. He became the 265th Pope in 2005 following his predecessor John Paul II's death.
The Pope is spiritual leader of the estimated 1.2 billion followers of the Catholic Church, according to the Annuario Pontificio, its annual statistical report.