A Vatican communique added that Francis had accepted Bishop Bransfield's resignation and handed executive responsibility of the Diocese of Wheeling-Charleston to Archbishop Lori as an apostolic administrator.
Cardinal DiNardo said he wanted to present an "action plan" to the pope to facilitate reporting of abuse and misconduct by bishops.
The USCCB headquarters in Washington, D.C., released a short statement more than three hours after the meeting saying the pope had "listened very deeply from the heart" as they spoke to him in "a lengthy, fruitful and good exchange" about how the US church had been "lacerated by the evil of sexual abuse".
Archbishop Georg Gaenswein, private secretary to Pope Emeritus Benedict XVI, on Tuesday described sexual abuse against minors by clergy as the Church's "own 9/11".
Francis removed McCarrick as a cardinal in July after a USA church investigation found the allegation credible.More news: Nintendo to sell NES-style Switch wireless controllers to online service subscribers
Mr DiNardo has said recent accusations of top Vatican officials, including the current pope, covering up for McCarrick deserve answers.
The head of the Pontifical Commission for the Protection of Minors, Cardinal Sean O'Malley, and two USCCB officials will also attend today's meeting.
The Archbishop of Washington has said he will travel to Rome to ask the Pope to consider accepting his resignation.
McCarrick is accused of molesting an altar boy and having seminary students sleep in his bed with him.
On the eve of the USA audience, Francis announced he was summoning the presidents of bishops conferences around the world to a February summit to discuss prevention measures and protection of minors and vulnerable adults.
In the United States, a group of 5,000 Catholic chief executives have frozen US$820,000 (€700,000) in funds paid annually to the Holy See pending clarification of the sex abuse cases.More news: Forza Horizon 4 is getting a James Bond day one auto pack
The video clip showed the 75-year-old prelate giving a speech during which he drew attention to the recent sex abuse scandals involving the church, notably in the USA state of Pennsylvania.
DiNardo has said that he wants the pontiff to authorize a full-fledged investigation of the McCarrick case and the allegations of a coverup by the Vatican.
The men told the pope how the US Church "is lacerated by the evil of sexual abuse".
An earlier comprehensive investigation into clergy sex abuse resulted in the 2004 John Jay report, which found that over 80 percent of abuse was committed against male victims, which has been used to underscore the predominantly homosexual nature of the clerical abuse crisis.
The revelation was the latest twist in an incredible turn of events in the US church that began with the June 20 announcement that one of the most prestigious USA cardinals, Theodore McCarrick, had been accused of groping a teenage altar boy in the 1970s.More news: Breanna Stewart Named WNBA Finals MVP As Seattle Storm Sweeps Washington Mystics