The two US bishops' resignations follow the 2012 jailing of Minnesota priest Curtis Wehmeyer for the sexual abuse of minors he preyed on during camping trips and possession of child pornography.
Wehmeyer's conviction led to the archdiocese of Saint Paul and Minneapolis being charged on June 5 with six counts of failing to protect minors after prosecutors unveiled substantial evidence that senior Church officials failed to act on repeated warnings from parents and others that the priest was a danger to children.
A former papal ambassador to the Dominican Republic will be tried for paedophilia next month in the first case of its kind to be brought before a Vatican court.
The first hearing in the trial of Jozef Wesolowski has been scheduled for July 11, 2015.
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The Polish former archbishop is accused of possession of child pornography in Rome in 2013-14 and the sexual abuse of minors during his 2008-13 spell as the Church's representative in the Dominican Republic.
He was defrocked by a church court in June 2014 but remained at liberty until September 2014, when he was placed under house arrest under an order which the Vatican described as coming directly from Francis.
Possession of child pornography has been a crime under the Vatican city state's penal code since 2013 under a change also initiated by Francis.
In a statement, the Vatican said its prosecutor had worked in collaboration with authorities in the Dominican Republic, who have failed in their attempts to have Wesolowski extradited to face trial there.
"This will be a delicate and detailed procedure, requiring the most careful observations and insights from all parties involved in the trial.