During his visit to Panama, Pope Francis also pledged support for "all efforts" to avoid further suffering in crisis-torn Venezuela and insisted public officials live simply, honestly and transparently.
"The abuse of minors is one of the vilest and most heinous crimes conceivable," the head of the global Catholic church said in his annual address to ambassadors to the Vatican.
"To those who abuse minors I would say this: convert and hand yourself over to human justice, and prepare for divine justice," Pope Francis said. His statement is the strongest yet on an issue testing the Church.
The resignation of Los Angeles bishop Monsignor Alexander Salazar is the latest in a string of cases of alleged misconduct against bishops to come to light this year, following the scandal of ex-Cardinal Theodore McCarrick.
The two are Cardinal George Pell of Australia and Francisco Javier Errazuriz of Chile. Both have been the subject of allegations related to sexual abuse - accusations they deny.
The deal gives the Holy See a decisive role in the appointment of all bishops in the country. The Vatican said Pope Francis recognised the legitimacy of the seven remaining state-appointed Chinese bishops.
After weeks of relative silence, Pope Francis has agreed to meet a delegation of US bishops and cardinals to discuss the Vatican response to the clergy abuse crisis.
Archbishop Carlo Maria Vigano said he told Pope Francis of sex abuse committed by a cardinal in 2013.
The Vatican was rocked again this month by devastating child sex report which accuses over 300 priests in the US state of Pennsylvania of abusing over 1,000 children since the 1950s.
Pope Francis has appealed to Catholics around the world to help root out the scourge of child sexual abuse. In an unprecedented letter, he said "we did not act in a timely manner, realizing the magnitude ... of the damage done to so many lives."
If passed, the legislation will allow elective abortions in the first 14 weeks of gestation. Argentina currently allows it only in cases of rape or risks to a woman's health.
Philip Wilson, 67, was found guilty in May of concealing abuse by paedophile priest Jim Fletcher in the Hunter region of New South Wales state during the 1970s by failing to report allegations against him.
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