Weakland, who had adopted a zero tolerance policy toward abusive priests, made the statement after ABC reported that he agreed in 1998 to pay $450,000 to a man who accused him of sex assault.
"Because I accept the agreement's confidentiality provision, I will make no comment about its contents," he said in his statement.
Weakland had reached the mandatory retirement age of 75 in April and is awaiting the Vatican's appointment of a new leader.
Both the pope and the Vatican's chief spokesman were traveling in Bulgaria Thursday, and another Vatican spokesman in Rome could not immediately be reached for comment.
The statement came a day after the Roman Catholic bishop of Lexington, Ky., temporarily stepped aside from his pastoral duties in the wake of a lawsuit over alleged sexual abuse. Also this week, two Roman Catholic priests, in New York and Maryland, have been arrested for alleged abuse.
In his statement, read by archdiocesan spokesman Jerry Topczewski, Weakland denied accusations made by Paul J. Marcoux, 53, on ABC's "Good Morning America."
"I have never abused anyone. I have not seen Paul Marcoux for more than 20 years," Weakland said.
Marcoux told ABC the agreement with Weakland, one of the U.S. church's leading liberals, had required him to keep silent.
"I was involved in a cover-up. I accepted money to be silent about it, not to speak out against what was going on," Marcoux said.
He said he was sexually assaulted about 20 years ago, when he was a student at Marquette University and went to the archbishop seeking advice about entering the priesthood. He told the network Weakland "started to try and kiss me and continued to force himself on me, pull down my trousers and attempted to fondle me."
"Think of it in terms of date rape," Marcoux told ABC.
ABC said as part of the settlement, the archbishop and the archdiocese denied the claims. The archdiocese declined to comment.
In its report, ABC quoted from an 11-page handwritten letter dated Aug. 25, 1980. The letter, which according to ABC was written by Weakland, said he could not pay more than $14,000 to settle the case.
"I should not put down on paper what I would not want the whole world to read. But here goes anyway," the letter said.
"I felt like the world's worst hypocrite. So gradually I came back to the importance of celibacy in my life."
Weakland has been under renewed criticism for how he dealt with a sexually abusive Roman Catholic priest in 1979.
In a newly released court document, Weakland said he moved the Rev. William Effinger to a new church after the priest admitted molesting a 13-year-old boy.
Last month, with sex abuse scandals battering dioceses across the country, Weakland wrote a letter apologizing to anyone who was sexually abused by a priest and appointed a commission to review allegations of sexual abuse in the archdiocese.
Weakland, whose archdiocese serves 685,000 people, has been a liberal force in the church. In the 1980s, he helped draft a controversial pastoral letter describing poverty in the United States as a moral scandal.
He was censured by the Vatican for studying why women have abortions and has suggested the church discuss allowing the ordination of married men to solve the priest shortage. He also has pushed for the church to give women a greater role.
In Kentucky, Bishop J. Kendrick Williams took administrative leave and strongly denied allegations that he abused anyone.
"Let me state this simply: the allegations are false," Williams said in a statement.
Bishop Anthony O'Connell of the Palm Beach, Fla., diocese resigned in March after admitting to sexual misconduct years earlier in another state. He was the second bishop of Palm Beach to resign over a sex scandal in the last four years.
Hawaii's Joseph Ferrario in 1989 was the first U.S. bishop accused of molestation. His accuser sued, but a court dismissed it as too late. Ferrario denied the charges and retired early in 1993.
Cardinal Roger Mahony of Los Angeles was accused of abuse this year, but police cleared him of the accusation.
An appeals panel in Massachusetts refused to reduce defrocked priest John Geoghan's nine- to 10-year sentence for groping a boy, a punishment his lawyer called overly harsh.
A suspended Maryland priest was arrested Wednesday night on charges of felony child abuse and sex offenses for allegedly molesting an 11-year-old boy in 1980.
The Rev. Brian M. Cox, 63, was taken into custody near his home at Resurrection Farm, a ministry to homeless people and families that he runs near Westminster, Md.
Police said the abuse happened while Cox was at St. John Catholic Church in Westminster. Cox was removed from the ministry in 1995, when similar allegations arose involving another youth. No charges had been filed.
A Catholic priest in New York surrendered to investigators Thursday on charges of sexually abusing a 12-year-old girl, Brooklyn District Attorney Charles Hynes said.
The Rev. Francis X. Nelson, 38, was indicted on two counts of second-degree sexual abuse and one count of endangering the welfare of a child in connection with an alleged 1999 incident, Hynes said in a statement.
Nelson, a priest at St. Charles Borromeo Church in Manhattan, allegedly grabbed the girl's chest and pressed his genitals into her buttocks on a visit to her Brooklyn home in May 1999.