Pope Francis has ordered an investigation of an American bishop accused of sexual misconduct and accepted his resignation, deepening a worldwide clerical abuse scandal.

The Vatican and US church officials announced the investigation as the pope was meeting US Catholic Church leaders to discuss a scandal that has shaken his papacy.

The Vatican said the pope had appointed Archbishop William Lori of Baltimore to run the Wheeling-Charleston diocese, West Virginia, until Bishop Michael J Bransfield is replaced.

There were no details on the specific allegations against Bishop Bransfield and neither he nor his legal representatives could immediately be reached for comment.

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The Catholic Church worldwide is reeling from crises involving sexual abuse of minors, deeply damaging confidence in the Church.

The archdiocese of Baltimore's website said the pope had ordered the archbishop to investigate allegations of sexual harassment of adults by Bishop Bransfield.

"My primary concern is for the care and support of the priests and people of the Diocese of Wheeling-Charleston at this difficult time," Archbishop Lori said in a statement.

"I further pledge to conduct a thorough investigation in search of the truth into the troubling allegations against Bishop Bransfield and to work closely with the clergy, religious and lay leaders of the diocese until the appointment of a new bishop," he said.

The announcement of Bishop Bransfield's resignation came while the pope was meeting Cardinal Daniel DiNardo, president of the US Conference of Catholic Bishops (USCCB), Cardinal Sean O'Malley of Boston, and Archbishop Jos Horacio Gomez of Los Angeles.

In a statement afterwards, Cardinal DiNardo said they told the pope of "our situation in the United States - how the Body of Christ is lacerated by the evil of sexual abuse." He called the meeting "a lengthy, fruitful, and good exchange".

Cardinal DiNardo had asked for the meeting after Archbishop Carlo Maria Vigano last month accused the pope of knowing for years about sexual misconduct by former Cardinal Theodore McCarrick and of doing nothing about it.

In July, the retired archbishop became the first cardinal to resign in nearly 100 years after American Church officials said allegations that he had sexually abused a 16-year-old boy almost 50 years ago were credible and substantiated.

The former leader of the Diocese of Washington DC has said that he had "absolutely no recollection" of the alleged abuse of the teenager but has not commented on the other allegations against him.

Cardinal DiNardo has called for the Vatican to launch an investigation, known as an "apostolic visitation," into how Archbishop McCarrick could have risen steadily through the ranks of the US church although many people knew that he had engaged for years in sexual misconduct with adult male seminarians.