VATICAN CITY — Cardinal Bernard Law, who resigned in disgrace as Boston’s archbishop in 2002 after the priest sex abuse scandal exploded in the United States, has retired from his subsequent job as head of a major Roman basilica.

The Vatican said today that Pope Benedict XVI had accepted the 80-year-old Law’s resignation as archpriest of St. Mary Major basilica and had named Spanish Monsignor Santos Abril y Castello to replace him.

Law’s 2004 appointment as the archpriest of one of Rome’s most important basilicas had been harshly criticized by victims of priestly sex abuse, who charged that bishops who covered up for pedophile priests should be punished, not rewarded.

Law turned 80 earlier this month. For a few years in the early 1960s, the newly ordained priest served as an associate pastor at St. Paul Catholic Church in Vicksburg.

While the pope could have kept him on longer — the dean of the College of Cardinals will be 84 this week, for example — he decided to replace him.

The Vatican announcement made no mention of Law’s resignation, though, merely noting in a perfunctory, two-line statement that Benedict had named a new archpriest for the basilica.

Law became the first and so far only U.S. bishop to resign for mishandling cases of priests who sexually abused children.

The crisis erupted in Law’s Boston in 2002 after church records were made public showing that church officials had reports of priests molesting children, but kept the complaints secret and shuffled some priests from parish to parish rather than remove them or report them.

The crisis spread as similar sexual abuse complaints were uncovered in dioceses across the country. To date, U.S. dioceses have paid out nearly $3 billion in settlements to victims and other costs.

Law himself was named in hundreds of lawsuits accusing him of failing to protect children from known child molesters. After 18 years leading the nation’s fourth-largest archdiocese, Law resigned in 2002, having asked Pope John Paul II twice before receiving permission to step down.

Ten months after he left office, Law’s successor, now-Cardinal Sean P. O’Malley helped broker an $85 million settlement with more than 550 victims of pedophile priests.

While in Rome, Law has been a frequent presence at all major Vatican ceremonial and diplomatic events, a lifestyle that galled many abuse victims who have long insisted that the Vatican crack down on bishops who transfer abusive priests rather than report them to police.

Law’s successor at St. Mary Major — one of the four basilicas under the direct jurisdiction of the Vatican — retired earlier this year as the Vatican’s ambassador to Slovenia and Macedonia.

Abril y Castello, 76, is also the No. 2 prelate who helps take care of matters dealing with a papal death and runs the Vatican until a new pontiff is elected in a conclave.

Now that he is 80, Law can no longer vote in a conclave, but he remains a cardinal.