"I seek with you God's forgiveness for the faults of Catholics throughout the history of this archdiocese," Law said in a cathedral packed with parishioners, Jews, blacks and Muslims.
"Let us kneel before God and acknowledge with sorrow the failures of the past and implore forgiveness for our own sins and shortcomings."
The apology came as Roman Catholic leaders from across the country, taking their cue from Pope John Paul II, express regret for failings as old as the 2,000-year-old church.
The church has been reflecting on its history during its Jubilee year, and the pope and others have decided to voice apologies for past and present sins during the season of Lent, a period of penance.
In Rome on Sunday, the pope expressed regret for anti-Semitism, the Crusades, the Inquisition and other "faults of the past."
While some critics have complained that the gestures are too little, too late, there was only praise from those attending Law's prayer service at the Cathedral of the Holy Cross in Boston's South End neighborhood.
"It's really a wonderful step forward on the part of the church to try to create greater reconciliation between the Jewish and Catholic communities," said Rabbi Samuel Chiel of Temple Emanuel.
Imam Taalib Mahdee, a Muslim leader, called the apology "a blessing of God."
"We pray that his prayers are answered," he said.
During the service, Law and other recounted Catholics' complicity in slavery, sexual abuse by priests, racism, anti-Semitism and the treatment of women.
By Laura Vozzella
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