"We write today seeking a different kind of meeting -- one in which our respective organizations -- yours, huge and struggling, and ours, small and struggling -- can begin to work together to safeguard children across the globe."
Meanwhile, in Los Angeles, one alleged victim of priest sex abuse, Michael Duran, urged Pope Francis to give Catholics new hope and make priests and cardinals accountable for their actions in cases where children have been sexually abused by clergymen.
Duran said he was sexually abused for three years by a Los Angeles Archdiocese priest beginning in 1983, when Duran was 11.
He and three other men allegedly sexually abused as boys by the same priest settled their lawsuits for $9.9 million against the archdiocese, Cardinal Roger Mahony and the now defrocked priest. Mahony was among the 115 cardinals in Rome who participated in the papal election this week.
Duran said he felt vindicated by the settlement. He and his attorney said authorities should investigate Mahony for his handling of child abuse complaints against the former priest, Michael Baker. The priest, who couldn't be reached for comment, served a prison sentence for molesting boys, Duran's attorneys said.
The 76-year-old leader, who served as the archbishop of Buenos Aires, is the first pope to take the name in honor of St. Francis of Assisi, revered among Catholics for his work with the poor.
The pontiff is a follower of the church's most social conservative wing. As a cardinal, he clashed with the government of Argentine President Cristina Fernandez de Kirchner over his opposition to gay marriage and free distribution of contraceptives.
He was runner-up in the 2005 papal conclave, behind then-Cardinal Joseph Ratzinger.
The new pope brings together the first and the developing worlds. Latin America is home to 480 million Catholics.
Francis' first public appearance as pope -- when he appealed for the crowds to pray for him before he gave a blessing -- suggested a "different pastoral style" in comparison with the more academic approach of Benedict, said Lombardi.
Francis is someone who has had "a day-to-day link with the population and ordinary people" during his many years at the head of a large diocese in Buenos Aires, he said.
He also sought to dampen concerns prompted by media reports that the new pope has only one lung.
Although Francis had part of one lung removed when he was a young man, the whole lung was not removed and the new pope is in good health, Lombardi said.
CNN iReporter Cesar Sotolongo in Lima, Peru, said the election of a Latin American pope, particularly from the Jesuit order, marked "a new chapter" for the Catholic Church.
Originally from Florida, Sotolongo also has his own advice for Francis: "The pope should shape the church with what he has been doing during his career (as an example)," he said. "Stay in contact with the people, communicate clearly, promote the unification of faith and ... represent the word of Jesus."
A Jesuit pope
Born in Buenos Aires to an Italian immigrant father, Francis is known for his simplicity.
Details given by Lombardi on Thursday of Francis' first hours as pope reinforce that impression -- one which may go down well with his global flock, many of whom live in poverty or are feeling the squeeze of austerity.
Francis stood, rather than sitting on a throne, to receive the oath of allegiance from his fellow cardinals after his election, and for his appearance on the balcony wore just a white cassock and a simple cross, eschewing gold or jewels, Lombardi said.