In a statement posted on the website of the Archdiocese of Los Angeles, Cardinal Mahony also said a special working group identified about 50 other nonessential church properties that could be sold to fund settlements, the International Herald Tribune reports.
Those properties are not being used by any parishes, and no schools, parishes or ministries would be shut down, he said.
"Though it has always been the position of the archdiocese that the insurance companies must honor their responsibility to fund a major share of future settlements, the archdiocese must be prepared to fund its share," Cardinal Mahony wrote.
The cardinal did not specify a timetable for settlement, but said he hoped the cases could be resolved in the "near future." Archdiocese spokesman Tod Tamberg declined to comment beyond Mahony's statement.
In December, the archdiocese paid $A80 million to settle 46 sexual abuse claims from two periods when the archdiocese had limited or no insurance against sexual abuse claims - before the mid-1950s and after 1987.
The archdiocese, which estimates it has 4.3 million Catholics, still faces more than 500 claims that have been in litigation for more than four years.
Seven major insurance companies have been negotiating with the archdiocese for years over whether they must pay to cover the lawsuits.
A spokeswoman for Survivors Network for Those Abused by Priests, or SNAP, said she believed Cardinal Mahony was attempting to shame alleged victims into quick settlements by holding the sale of church property over their heads.
Spokeswoman Mary Grant told reporters she also worried that Cardinal Mahony's statement would make the Catholic community feel "that something is being taken away from them" by alleged victims.
Code for rapists
In another story, Mexico City Cardinal Norberto Rivera Carrera, who has been accused in a US civil lawsuit of covering up child rape in Mexico and Southern California, has said that Roman Catholic Church officials used coded language to communicate about problem priests, McClatchy News reports.
In a court filing obtained by McClatchy, Cardinal Norberto Rivera Carrera, who oversees the Archdiocese of Mexico City, said he told Los Angeles Cardinal Roger Mahony that a priest who is now wanted on criminal charges of child rape was moving from Mexico to Los Angeles for "family and health reasons".
"The phrase 'family and health reasons' was used within the Church to warn that a priest suffers from some sort of problem," Cardinal Rivera said in his written declaration.
Cardinal Rivera said he expected the phrase to trigger questions about the Rev Nicolas Aguilar, who had been forced to leave a parish in Mexico over suspected homosexual behavior.
"I anticipated that Cardinal Mahony would request a more detailed account of Fr Aguilar's history and problems if he decided to consider Fr. Aguilar as an employee of the Los Angeles Archdiocese," Cardinal Rivera said.
The reported communication between the clergymen about Aguilar took place two decades ago, but it us now at the heart of a civil lawsuit that accuses two of the world's most prominent Roman Catholic clergymen of conspiring to cover up sex crimes.
LA archdiocese to sell property to fund sexual abuse settlements (International Herald Tribune, 16/5/07)
Church 'code' for rapists? (Miami Herald, 16/5/07)
Catholic Dems protest Pope's abortion comments (USA Today, 16/5/07)
LINKS (not necessarily endorsed by Church Resources)
Los Angeles Archdiocese
LA Archdiocese settles abuse claims for $A75 million (CathNews, 4/12/07)
LA Cardinal calls sex abuse scandal a 'purification' (CathNews, 2/4/02)
Catholic US House Dems repudiate pope's abortion excommunication comments (Catholic Online, 16/5/07)
17 May 2007