(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. 
How many priests were threatened in the capital?
10