MEXICO CITY — Mexico’s Roman Catholic Church on Monday harshly criticized what it called a campaign to smear three priests murdered in less than a week by suggesting the victims had been involved in questionable behavior.

The outrage came in response to a state prosecutor’s allegations that two of the dead clerics had been drinking with their killers beforehand and media reports suggesting the third had last been seen with a young boy.

“In these cases it has become clear that state governments that cannot handle the drug cartels are criminalizing the victims, depicting some as drunks and another as a pedophile, making it look like the crimes were not related to drug cartels but because of some immoral conduct,” said the Rev. Hugo Valdemar Romero, spokesman for the Catholic Archdiocese of Mexico City.

“To physical death they are adding moral assassination, slandering the priests and holding them up to ridicule,” Romero said, “and that has caused deep indignation in the church,” Romero said.

Two of the slain priests were shot to death in Veracruz state last week and their bodies dumped on a roadside. On Sunday officials confirmed that the other priest had been shot to death in Michoacan state after being abducted.

Local media published a photo taken from security footage purportedly showing the priest at a hotel with a boy. But other reports later said the man in the image was not the priest. The Michoacan state prosecutors’ office did not respond to a request for comment on the photo.

Cardinal Alberto Suarez Inda, who heads the archdiocese in Michoacan, defended his priest’s character.

“The publication of some images and malicious interpretations has made the situation more painful,” he wrote Monday.

The Mexican Council of Bishops also urged authorities to investigate the killings without casting aspersions on the victims.

“We respectfully and urgently demand that the respective authorities get to the bottom of both cases … and with the same forcefulness, we demand that no priest, or anyone, be slandered, above all before the investigations are finished,” the council wrote.

Parishioners in the Veracruz city where the two priests were killed have also said they were skeptical of the prosecutor’s account and suspected an attempt to quickly shelve the case.

Romero said of the government, “the least we expect is a public apology.”

It is unclear whether drug gangs were directly involved in last week’s killings, though most attacks on priests in Mexico in recent years have occurred in areas plagued by cartel violence.

Prosecutors have suggested the robbery of a couple hundred dollars in church collections may have been a motive in the Veracruz killings.

But Cardinal Francisco Robles Ortega of the western state of Jalisco said priests there have been subjected to extortion demands, a common practice among drug cartels in Mexico.

Mexico’s Catholic Media Center says 28 priests have been killed in Mexico since 2006, not counting last week’s slayings. It says Veracruz, Guerrero and Mexico states are the most dangerous for priests; along with Michoacan, they are some of the state with the worst drug-cartel problems.