Mahony was described as calm and unflappable by the attorney who questioned him for more than three hours.
Recently released files show the former head of Los Angeles' Catholic Archdiocese maneuvered behind the scenes to protect pedophile priests in order to protect the church from scandal.
Mahony has apologized for those actions and contends he turned the archdiocese into a leader for safeguarding children.
Catholics United, joined by representatives from the Survivors Network of those Abused by Priests, delivered a petition to Mahony's home church, St. Charles Borromeo Church in North Hollywood, on Saturday, asking him recuse himself from the upcoming papal conclave. The petition had nearly 10,000 signatures.
"Cardinal Mahony, please stay home from the papal conclave and help bring healing to your people," said Chris Pumpelly of Catholics United.
Abuse victims and their supporters say Mahony's participation will send the wrong message.
"He shouldn't go to Rome," said Linda Roletti, a Catholic. "I think he should be put in shackles and taken away."
The Associated Press contributed to this report.