Attorney Anthony De Marco, representing a man suing the archdiocese, said Cardinal Roger Mahony answered questions under oath for more than 3 1/2 hours Saturday about how he handled clergy sex-abuse cases, the Los Angeles Times reported Sunday.
"He remained calm and seemingly collected at all times," De Marco said.
The deposition was the first time Mahony was asked about recently released internal records that indicated he shielded abusers from law enforcement.
The deposition occurred before Mahony was to leave for Italy to vote in the conclave that will elect a successor to Pope Benedict XVI, who is retiring at the end of February.
The cardinal said in a Twitter message he "will be tweeting often from Rome," the Times reported.
Mahony's deposition involved a Mexican priest, Nicholas Aguilar Rivera, who authorities say they believe molested at least 26 children during a nine-month stay in Los Angeles, the Times said. A trial is scheduled for April.
Recently released files indicated Aguilar Rivera fled to Mexico after Mahony aide Thomas Curry warned that parents likely would contact police and that the visiting priest was in "a good deal of danger." Aguilar Rivera is a fugitive in Mexico.
The archdiocese agreed that Mahony could be questioned for 4 hours about that case and about 25 other priests accused of abuse during the same period, the Times said.
A Catholic organization delivered a petition Saturday that contained thousands of signatures asking that Mahony recuse himself from the conclave in Rome, the Times said.
A spokesman for Catholics United said the group collected nearly 10,000 signatures asking that Mahony not participate because of the scandals that occurred while he led the archdiocese.