The time and place of the apology by Milwaukee Archbishop Rembert Weakland has not been determined, spokesman Jerry Topczewski said.
Pope John Paul II accepted Weakland's resignation Friday in a decision announced in the daily news bulletin of the Holy See's press office, citing Weakland's age, 75, as an explanation.
The archbishop, a leading liberal in the church, is the highest-ranking U.S. churchman to acknowledge a settlement of an allegation against him.
Weakland said Thursday that he paid a $450,000 settlement to Paul Marcoux, a former theology student who accused him of sexual assault more than 22 years ago. Weakland denied ever molesting anyone, but asked the Vatican to expedite the resignation he submitted earlier this year after reaching the mandatory retirement age of 75.
Topczewski said Weakland was sorry for any pain the settlement caused.
"He's remorseful for the strain and stress this brought on the archdiocese and the church," Topczewski said.
Milwaukee's top prosecutor, E. Michael McCann, said he had known for years that Weakland had a relationship with a man, but there was no suggestion of any crime.
"He advised me that he had a relationship that had compromised him in some fashion," McCann told the Milwaukee Journal Sentinel newspaper for its Friday editions. "He was troubled by it, but there was nothing criminal in it."
McCann said he may ask for a special prosecutor to investigate where Weakland got the $450,000 he allegedly paid to Marcoux.
McCann said the payment Weakland made to Marcoux in 1998 needs to be explored to make sure it did not involve money that was committed to charity or other causes or expenses. Milwaukee, like other urban areas, has seen schools and churches in poor areas consolidated as people leave the city for the suburbs.
Weakland did not say where he got the funds for the settlement but noted that he had during his 25-year tenure as head of the Milwaukee Archdiocese earned far more than the amount involved in honorariums and other revenue from lectures and writings, which he turned over to the archdiocese.
Roman Catholics struggled to absorb the news after Marcoux went public Thursday with word of the settlement.
"I want to cry and crawl under my bed," said Marquette Law School Dean Howard Eisenberg, who heads a commission Weakland created to review sex abuse allegations against priests.
Weakland formed the commission in March, and in April announced the archdiocese would adopt a no-tolerance policy toward molestation.
Bishop Wilton Gregory, president of the United States Conference of Catholic Bishops, said Friday he was "deeply saddened" by the news.
"It comes at a time when the church in our country is suffering greatly from what seems to be an unending series of revelations and accusations," Gregory said.
Marcoux, now 53, said he and Weakland had had several drinks the night of the alleged assault in 1979, when Marcoux was a university student in his 30s. He said he did not go to police because two priests — a cousin and a friend — advised against it.
In a statement Thursday, Weakland denied the claims. "I have never abused anyone. I have not seen Paul Marcoux for more than 20 years," he said.
"Because I accept the agreement's confidentiality provision, I will make no comment about its contents."
The pope was traveling in Bulgaria when the Vatican's announcement was made. His spokesman, Joaquin Navarro-Valls, said John Paul was abreast of developments in the Weakland case.
No successor has been named, but Bishop Richard Sklba will be in charge until a group of priests elects an interim administrator.
Cardinal Walter Kasper, a top Vatican official traveling with the pope, said "I pray for the American bishops to find a solution to this crisis, and I'm sure they will find one."
Asked what he was proposing, Kasper replied: "I can't propose a solution for them."
In recent years, a dozen Roman Catholic bishops worldwide have been publicly accused of misconduct. Weakland's case stands out in part because of his stature in the church.
It was just last month that the pope summoned the U.S. cardinals and top leaders to Rome to discuss the sex scandal that has shaken the American church. The cases that have drawn the most attention and condemnation involve pedophilia, though a number of other lawsuits and allegations involving assaults or relationships with adults have also emerged.
The U.S. bishops are to meet in Dallas in mid-June to discuss among other things a new policy for handling sexual abuse by the clergy, one that may involve a "zero tolerance" for offenders.
Weakland, a leading liberal in the U.S. Catholic Church, said he asked that his retirement be expedited so his case would not distract attention from efforts to restore credibility to the church.