(CNN) -- The threatening calls reportedly came one after the other to Mexico's main Catholic seminary.
Callers, claiming to be from one of the country's feared drug cartels, offered an ominous warning: Pay up if you value the safety of your priests.
"They called several times. They identified themselves as the Familia Michoacana, but who knows?" Cardinal Norberto Rivera, archbishop of Mexico City, revealed at a Mass this week. "I spoke with the authorities. We made the appropriate report. Because they wanted us to pay. Because if not, they would kill one of us. They wanted to extort 60,000 pesos ($4,600)."
Reports of extortion have become increasingly common as drug cartels expand their reach in Mexico. But public denouncements of such attempts are rare.
Rivera called on parishioners to report extortion to authorities, and he urged them not to pay.
His description Sunday of the extortion attempts and a statement denouncing drug violence give a glimpse into the problems faced by a Catholic Church often caught in the crossfire of warring cartels and government efforts to stop them.
In the country's capital alone, more than 10 priests have been threatened with extortion, said the Reverend Hugo Valdemar Romero, a spokesman for the archdiocese.
"None of them have paid," he told CNN. "Last year, two extortionists were arrested."
It's not uncommon for individual parishes to face extortion threats, he said. But the calls last month to the Seminary of the Archdiocese of Mexico marked the first time such a large church-run institution in the capital had been targeted, Romero said.
Mexico's Catholic priests have long struggled with how to deal with spiraling drug violence and cartel culture.
In addition to widespread extortion attempts by gangs, church officials have said clergy have received threatening notes and telephone calls after sermons against drug use and trafficking.
In 1993, Cardinal Juan Posadas Ocampo was gunned down in the parking lot of an airport in Guadalajara, Mexico. Authorities said a drug gang had confused him with a rival trafficker, but some church leaders claimed he was targeted for denouncing drug trafficking.
In 2009, Hector Gonzalez, the archbishop of the northern state of Durango, raised fears of attacks on the clergy after he said that Mexico's most wanted man, Sinaloa cartel boss Joaquin "El Chapo" Guzman, lived in a Durango town and that "everybody knows it except the authorities."
Days later, investigators found the bodies of two slain military lieutenants in mountains nearby, accompanied by a note: "Neither the government nor priests can handle El Chapo."
Gonzalez quickly backed away from his comments, telling reporters who asked him about them, "I am deaf and dumb."
There's also a flip side. Some critics say churches have received large donations from traffickers.
A plaque inside a chapel in Mexico's Hidalgo state once boasted a donation from Heriberto Lazcano Lazcano, a leader of the Zetas cartel until his death last year in a shootout with Mexican forces.
This year, even as government officials have suggested that drug-related violence could be on the decline, church leaders have warned that priests and the congregations they serve remain at risk.
Authorities arrested four suspects after the priests were found slain inside their parish.
A group of Mexico's Catholic bishops have said they plan to discuss the violence with Pope Francis during a visit to the Vatican next year.
CNN's Mariano Castillo and CNNMexico.com contributed to this report.