DUBLIN—Swimming against the tide of promises to crack down on abuse and cover-up led by Pope Francis, a newly created Mexican cardinal said that some accusers should be “ashamed” to point their finger at clerics because many of them have skeletons in their own closets.

The victims of pedophilia who “accuse men of the Church should [be careful] because they have long tails that are easily stepped on,” said Cardinal Sergio Obeso Rivera.

The cardinal, emeritus Archbishop of Xalapa, in Veracruz, Mexico, spoke to journalists before a celebration he led in his former diocese.

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Even though he acknowledged that some allegations are true, he went after the victims and avoided referring to the Pennsylvania grand jury report in the United States that found some 300 abusive priests in a span of seven decades in six dioceses.

Obeso Rivera’s words came last week, after the report was made public.

“I’m here happy to talk about nice things, not about problematic things, it’s an accusation that is made, and in some cases it’s true. But the evil of many is the consolation of fools, because sometimes those who accuse men of the Church should [be careful] because they have long tails that are easily stepped on.”

However, he did say that the accusations “make us feel bad and we want to improve.”

Obeso Rivera was made a cardinal by Pope Francis on June 28. As the prelate is over 80, he will not be participating in the eventual conclave to choose the pontiff’s successor.

Mexico is the home of Father Marcial Maciel Degollado, founder of the Legionaries of Christ, who was found guilty by the Vatican of having sexually abused minors and young men. After his death, it was also revealed that he had maintained relationships with at least two women, fathering more than one child.