At a prayer vigil attended by some 60,000 young people in Lima's national stadium, the pope walked among the crowd to greet people as thousands held up their phones as torches.
He knows the scandal from his years as a missionary and bishop in the country he calls his"homeland.".
An account of a gathering during the visit said those present reflected on how to foster a shift in mindset —"by listening to victims, seeking the truth, pursuing paths towards healing, and committing to the creation of safe environments.".
Thousands more, including children dressed as the pope or as bishops, lined the route for a glimpse of him as he passed in the popemobile.
Leo, head of the world's 1.4 billion Catholics, is on a six-day visit that will take him from the deep Amazon to the high Andes.
The stop is part of a three-nation Latin American tour on which he has not avoided sensitive political and social topics.
He is due to make an emotional return to Chiclayo, the northern city where he was bishop for a decade.
During his years in Peru, then known as Prevost, he worked in poor and remote northern areas and stayed close to local communities in times of hardship, sometimes reaching them on horseback.
He is also scheduled to visit Cuzco, at more than 3,400 metres (11,000 feet), a stop that will test his recovery from lung surgery.
The journey mixes a personal return with public appeals on abuse, the place of women, and the strains facing Peruvians.