Police on Tuesday arrested a priest in DiNardo's Texas diocese following allegations he abused a male high school student between 1998 and 2001.
Wuerl, who was bishop of Pittsburg for some 18 years, offered to resign almost three years ago when he turned 75 but Francis hasn't accepted it.
All bishops are required to submit their resignation at the age of 75, but the Pope does not have to accept it.
Some clergy from the Catholic Church have been carrying out abuse for decades.
"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.
The Catholic Church worldwide is reeling from crises involving sexual abuse of minors.
Wuerl's name was mentioned several times in the report for allegedly not doing enough to remove some predator priests from ministry. He admitted to sex abuse survivors that he had been "part of the problem" in that instance.
Wuerl has also been embroiled in the allegations of molestation leveled at former Cardinal Theodore McCarrick.
After the allegations against McCarrick were publicised in June, it emerged that it was apparently an open secret - including at the Vatican - and that he routinely molested seminarians and young priests and harassed them. Many have called for Wuerl's resignation since the report was released.
The current Washington Cardinal has remained adamant he had no idea until recently.
The church did not provide additional information about the allegations Bransfield faces.
The summit was announced a day before Francis will meet American church leaders hit by fresh accusations over the cover-up of sex abuse by priests.
After weeks of relative silence, Pope Francis has agreed to meet a delegation of USA bishops and cardinals to discuss the Vatican response to the clergy abuse crisis.
It will take place in Rome on the 21-24 February 2019.
Pope Francis will meet at the Vatican with leaders of the U.S. Catholic Church, including the president of the U.S. Conference of Catholic Bishops, Cardinal Daniel DiNardo, to discuss clergy sexual abuse.
In an explosive 11-page letter, Archbishop Viganò, the former apostolic nuncio to the U.S., accused Pope Francis of lifting sanctions that were placed upon the former D.C. Cardinal McCarrick during Pope Benedict's reign, going so far to making him a close adviser.