More recently, Francis's papacy was hit by accusations from a retired Vatican ambassador that he helped a top American cardinal evade sanctions imposed by Pope Benedict for molesting and harassing adult seminarians.
There were no details on the specific allegations against Bransfield and neither he nor his legal representatives could immediately be reached for comment.
The council has been meeting with Francis over the last three days and on Monday expressed their "full solidarity" with the Pope noting that the Vatican was preparing a response to an explosive dossier from Archbishop Carlo Maria Viganò.
The Catholic Church worldwide is reeling from crises involving sexual abuse of minors.
Separately, the Diocese of Wheeling-Charleston said on its website that Mr Bransfield, 75, will be investigated over "allegations of sexual harassment of adults". His statement said the group told Francis the US church was "lacerated by the evil of sexual abuse".
But first Pope Francis will meet with the head of the USA bishop's conference and other top U.S. church officials on Thursday to discuss the sex abuse scandal.More news: ‘Just stand’: Army vet launches t-shirts with ‘patriotic’ message for Kaepernick & Nike
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Abuse scandals have also shaken the Catholic Church in Australia, Chile and Ireland, among other countries.
In a statement issued Thursday regarding the case of Bransfield, Lori said: "My primary concern is for the care and support of the priests and people of the Diocese of Wheeling-Charleston at this hard time", Catholic News Service reported. The archbishop will perform both roles until a new bishop is appointed and in place.
In July, Washington Cardinal Theodore McCarrick resigned amid claims of abuse.
The head of the U.S. Conference of Catholic Bishops, Houston Cardinal Daniel DiNardo, had requested the papal audience last month following revelations that McCarrick had risen through church ranks even though the allegations of sexual misconduct were known in U.S. and Vatican circles.
Christian blogger, speaker and writer for The Daily Wire, Matt Walsh joined Glenn on today's episode of "The Glenn Beck Radio Program", to react to the pope's controversial speech and weigh in on the far-reaching sexual abuse scandals within the church.
McCarrick is accused of sexually abusing a teenager in the 1970s and young religious workers.
DiNardo has said Vigano's accusations "deserve answers that are conclusive and based on evidence".