The cardinal, who retired as archbishop of Los Angeles in 2011, also said in a statement Monday that he prays for victims of abuse by priests daily as he celebrates Mass in his private chapel.
"It remains my daily and fervent prayer that God's grace will flood the heart and soul of each victim, and that their life journey continues forward with ever greater healing," he said, explaining that on his altar he keeps cards with the names of each of the 90 victims he met with from 2006 to 2008.
"As I thumb through those cards I often pause as I am reminded of each personal story and the anguish that accompanies that life story," Mahony said.
"I am sorry," the cardinal's statement concluded.
Mahony's comments followed the publication by the Los Angeles Times and The Associated Press portions of documents filed in court as part of a lawsuit against the archdiocese. Some of files showed archdiocesan officials worked to conceal child molestation by priests from law enforcement authorities in the 1980s.
The release came two weeks after a Superior Court judge's ruling that the names of personnel identified in the files could be made public. Judge Emilie Elias' Jan. 7 ruling overturned an earlier decision by a retired federal judge who, acting as a mediator in a settlement between the archdiocese and those who claimed they were sexually abused, said that material to be released should have names redacted to prevent the documents' use to "embarrass or ridicule the church."
Church officials in Los Angeles had fought for years to keep the files private.
The 2007 settlement for $600 million covered more than 500 people who made claims about being sexually abuse by priests and other church personnel. Some of the priests who had claims against them sued to keep their names from being released, saying it violated their privacy rights.
While the archdiocese's actions to protect priests accused of abuse and its reluctance to work with investigators is known, the documents offer a closer look at the efforts undertaken to safeguard accused clergy.
Memos exchanged in 1986 and 1987 by Mahony and Auxiliary Bishop Thomas Curry, who was the archdiocese's vicar of clergy and chief adviser on sexual abuse cases at the time, reveal proposals to keep police from investigating three priests who had admitted to church officials that they molested young boys, the Los Angeles Time reported.
The documents show that Curry suggested to Mahony that they prevent the priests from seeing therapists who might alert authorities and that the priests be given out-of-state assignments to avoid criminal investigators.
The newspaper said the memos were from personnel files for 14 priests.
Files of at least 75 more accused abusers are to become public in coming weeks under the terms of the settlement.
The newspaper reported archdiocesan attorney Michael Hennigan said in a statement Monday that church policy in the late 1980s was to let victims and their families decide whether to go to police.
"Not surprisingly, the families of victims frequently did not wish to report to police and have their child become the center of a public prosecution," he said.
Hennigan also said that memos from that era "sometimes focused more on the needs of the perpetrator than on the serious harm that had been done to the victims."
"That is part of the past. We are embarrassed and at times ashamed by parts of the past. But we are proud of our progress, which is continuing," Hennigan said.
Mahony's statement, released through the archdiocese, said steps to safeguard "all children in the church began here in 1987 and progressed year by year as we learned more about those who abused and the ineffectiveness of so-called 'treatments' at the time."
"Nonetheless, even as we began to confront the problem, I remained naive myself about the full and lasting impact these horrible acts would have no the lives of those who were abused by men who were supposed to be spiritual guides," Mahony said.