Cardinal DiNardo said he wanted to present an "action plan" to the pope to facilitate reporting of abuse and misconduct by bishops.
The 81-year-old Jesuit Pontiff, the cardinal explained, "listened very deeply from the heart" during what was "a lengthy, fruitful, and good exchange". An archbishop has accused Francis himself of turning a blind eye to the alleged misdeeds of McCarrick, who has resigned from the College of Cardinals.
There were no immediate details of the allegations against Bransfield.More news: United States threatens ban to fight teenage vaping epidemic
Mr DiNardo has said recent accusations of top Vatican officials, including the current pope, covering up for McCarrick deserve answers. Accompanying them at the meeting was Boston Cardinal Sean O' Malley, who is president of the Vatican's Commission for the protection of minors.
Earlier this morning, news from Rome announced that the Pope will be summoning the presidents of the Catholic Bishops conferences from around the world - top officials of the Catholic Church - to discuss the escalating sexual abuse scandals dominating countless headlines. The request followed the release of the Pennsylvania grand jury report on sexual abuse cases in six Pennsylvania dioceses and the announcement of credible allegations of child sexual abuse committed by Archbishop Theodore E. McCarrick, the former cardinal-archbishop of Washington.
The Vatican press office said Pope Francis will have presidents of the Catholic bishops conferences convene at the Vatican from February 21 to February 24.
DiNardo's deputy Jose Horacio Gomez and general secretary Brian Bransfield also attended the closed-door meeting. Two dioceses also had announced allegations of inappropriate contact between Archbishop McCarrick and seminarians, resulting in settlements totaling more than $100,000.More news: Check out the official iPhone XS, XS Max and XR promo videos
House Speaker Paul Ryan (R-WI) commented Thursday on the sexual abuse and cover-up scandal that is rocking the Catholic church.
In a letter to priests in the diocese, Wuerl acknowledged Catholics' questions about their bishops' ability to lead them to healing amid a massive clerical sex-abuse crisis, the Washington Post reported on Tuesday.
Also Thursday, Francis accepted the resignation of Bishop Michael J. Bransfield of Wheeling-Charleston, W.Va., and ordered an investigation into accusations that Bransfield sexually harassed adults.
He added: "Elitism, clericalism fosters every form of abuse".More news: Russia, UN begin consultations on Syrian constitutional committee in Geneva
In Germany, a church-commissioned study detailed 3,677 abuse cases against minors, mostly boys, between 1946 and 2014, involving 1,670 clergy.