Francis's prayer at the Basilica Santa Maria Maggiore (St. Mary Major) in Rome comes after he promised the crowds in St. Peter's Square after his election that he would pray to the Madonna "that she may watch over all of Rome."
Argentinian Jorge Mario Bergoglio, the 76-year-old archbishop of Buenos Aires, was chosen by the conclave of cardinals on March 13 -- on the second day of voting.
The new pontiff, the first to take the name Francis, replaces retired Pope Benedict XVI, who last month became the first pope in 600 years to resign. Bergoglio reportedly finished second in the 2005 conclave that selected Benedict.
In his first address to the tens of thousands of believers huddled in the rainy night, Francis praised his predecessor.
"First of all I would like to pray for Benedict, our bishop emeritus," the pope said. "We pray altogether for him for God to bless him and for the Madonna to hold him."
Francis has also said he will visit Benedict, although a date for such a visit has not yet been announced.
Francis, the son of Italian immigrants, is known for his modesty. While serving as the archbishop of Buenos Aires he denied himself the luxuries that previous cardinals enjoyed.
He reportedly lived in a simple apartment, often rode the bus to work, cooked his own meals, and regularly visited slums that ring Argentina's capital.
His election was welcomed by political and spiritual leaders. U.S. President Barack Obama applauded the selection of the first pope from the Americas as a sign of the region's strength and vitality.
UN Secretary-General Ban Ki-moon said he hoped Francis would continue to promote interfaith dialogue.
"I look forward to continuing cooperation between the United Nations and the Holy See under the wise leadership of His Holiness Pope Francis," Ban said. "We share many common goals from the promotion of peace, social justice, and human rights to the eradication of poverty and hunger -- all core elements of sustainable development."
The Russian Orthodox Church welcomed the election and hoped "that relations between the Orthodox and Catholic churches will develop in a positive spirit."
The Dalai Lama expressed his "sense of joy" in a letter to Francis.
In a congratulatory message, China expressed hopes for improved ties with the Catholic Church, but it stressed the Vatican must take the initiative and end diplomatic relations with Taiwan.
As the new leader of the world's 1.2 billion Catholics, Francis faces many challenges, including sex scandals and falling membership, mainly in Europe.
Later on March 14, Pope Francis also met with the College of Cardinals in the Sistine Chapel, including the 115 princes of the church who elected him.