The ceremony in St Peter's Basilica on Tuesday featured testimony from an abuse survivor, who told hundreds of bishops in attendance that the abuse scandals "have shaken the faith of millions (and) tarnished the reputation of an institution that many look to for guidance".
Francis returned on Sunday from a trip to Belgium, where he faced some of the strongest criticism yet levied during one of his foreign trips.
The country's king and prime minister urged more concrete actions to address the abuse scandals, and leaders at two Catholic universities denounced the pope's stances on the role of women in the church and society.
As part of Tuesday's service, seven cardinals, the highest figures after the pope in the 1.4-billion-member global Church, made requests for pardon for different Church failings. Francis told attendees he wrote the requests himself "because it was necessary to call our sins by their first and last names".
Cardinal Sean O'Malley, the retiring archbishop of Boston who leads the Vatican's commission on clergy sexual abuse, asked forgiveness for abuse. Cardinal Kevin Farrell, a former bishop of Dallas who leads the Vatican's department for lay people, asked pardon "for all the times that we have not recognised and defended the dignity of women".
Francis said the service was intended "to begin to heal wounds that never stop bleeding".
"We ask forgiveness, feeling ashamed, from those who have been hurt by our sins," said the pope.
The Vatican summit, known as a synod, opens on Wednesday. The meeting includes cardinals, bishops and lay people from more than 110 countries. The synod members will vote on a final text in late October that may suggest doctrinal changes.
An earlier summit, held last year, featured discussions on divisive issues such as women's ordination and blessings for same-sex couples. But most of the hottest issues for this assembly have been assigned to study groups that will make final reports next June to Francis, who is 87.
