It required accusations of abuse to be reported to police and the permanent removal from ministry of any priest found to have abused a minor.
Bransfield came as the pontiff began a closed-door meeting in his private study with four United States bishops and cardinals to address the church's wave of sexual abuse crises, including a cover-up scandal that even implicated the pope himself.
Viganò's accusations came on the heels of a Pennsylvania grand jury report which detailed over 1,000 instances of sexual abuse by 300 priests and cover-ups by bishops.
A delegation of USA cardinals and bishops is already heading to the Vatican Thursday to meet with Francis over accusations from a retired Vatican ambassador that he rehabilitated a top American cardinal from sanctions imposed by Pope Benedict XVI for having molested and harassed adult seminarians.
The pope was scheduled to meet Cardinal Daniel DiNardo of Galveston-Houston, who leads the US Conference of Bishops, and Cardinal Sean O'Malley of Boston, who advises the pope on sex abuse issues.
Archbishop Lori will meet with clergy and lay leaders of the Diocese Thursday and Friday.
Just prior to their meeting, the pope accepted the resignation of West Virginia bishop Michael Bransfield and has authorized an investigation into allegations that he abused adults.More news: Apple shows off iPhone XS
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After hearing from his council, the pope "decided to convoke a meeting with the presidents of the bishops' conferences of the Catholic Church on the theme of the protection of minors", the council said in a written communique.
However, a pope is not obliged to accept such a resignation and Pope Francis has essentially kept Cardinal Wuerl in office in Washington ever since.
The Vatican is grappling with claims that the leader of the Catholic Church helped cover up an American cardinal's misconduct.
Wuerl is facing increasing scrutiny both over what he may have known about abuse allegations against his predecessor, former Cardinal Theodore McCarrick in Washington, and how he handled abusive priests while he headed the Diocese of Pittsburgh.
"Our discernment here, I believe, has indicated the way forward to bring healing and a new beginning at the service of this church", Wuerl said.
A study commissioned by the German bishops' conference reports the sexual abuse of thousands of children by priests and religious in that country over a period of 70 years.
Bishops, he said, should be men of prayer, and should know they were chosen by God and keep close to their flock.
The Archbishop of Washington has said he will travel to Rome to ask the Pope to consider accepting his resignation.