"The crisis of clergy sexual abuse of minors is not just a media-driven or public perception concern in the United States, but is a very serious issue undermining the mission of the Catholic church," Law said of the message he'll bring to Rome.
Law made his first public appearance in two weeks before departing for a rare gathering of U.S. cardinals at the Vatican on Tuesday and Wednesday.
CBS News Correspondent Gretchen Carlson reports that Boston became the center of the scandal when it came to light that Law, and others, repeatedly reassigned a priest accused of pedophilia.
"Some have likened the situation facing the Catholic church in Boston and across the country to last year's Sept. 11 tragedy, a crisis which shocks the heart and soul and which must spark immediate and decisive changes in order to prevent possible recurrence in the future," he said.
Across the country, several Catholic leaders used Sunday's services as an opportunity to share some parting words, encouragement and apologies before embarking for Rome.
Twelve of the 13 American cardinals will attend this week's meeting, convened by Pope John Paul II to discuss the sexual abuse scandal engulfing the Church.
"I think it's just awesome that the pope at his age and with his health is going to do something about it," said Harriet Kondziolka, a Catholic parishoner in suburban Chicago.
Law said it is "a clear signal the Holy See and church leadership in the United States recognize the gravity of the current situation."
"Despite the anger and broken trust that many feel toward me, and despite perceptions that next week is simply a gathering of aged conservative cardinals and Vatican officials, please know that as long as I am in position to do so, I will work tirelessly to address this crisis and to underscore its severity," he said.
"This is a wake-up call for the church," Law continued.
Law's remarks were met with applause by the approximately 600 parishioners in attendance. But outside the cathedral, about three dozen protesters called for his resignation and questioned the significance of the Rome summit.
"Nothing's going to come out of it," said Mike McGuire, 38, who was brought up Catholic. "It's just a meeting of the boys club. Too little, too late."
"Are they really waking up?" asked Suzy Nauman, 42, who carried a sign demanding Law's resignation. "I'm suspicious at this point. I really am."
In Rome, Pope John Paul II reminded a flock of new priests of their duties. You must be holy, he told them. "Perfect."
John Paul's exhortation was not unusual for a ceremony to ordain 20 new priests.
But ahead of this week's summit, it took on symbolic significance, highlighting the strict standards of fidelity to vows that the pope has set for churchmen — and which some in America are accused of breaking.
Jesus expects a "higher loyalty" from priests, a more rigorous poverty and humility, the pontiff told the new priests gathered in St. Peter's Basilica.
"He asks of you to be perfect, as your heavenly Father is perfect," he said. "In a word, the Lord wants you to be holy."
The pope appeared in particularly frail form during the two-hour Mass. Addressing pilgrims and tourists later in St. Peter's Square, his speech was even more slurred than usual, and at one point he appeared to have lost his place in the text.
Church officials have said the American scandal has deeply affected the pope, who turns 82 next month, suffers from the symptoms of Parkinson's disease, and has recently been forced to scale back his participation in long ceremonies because of knee pain.
While the ailing pope is not expected to take part in every meeting, CBS News Correspondent Allen Pizzey reports that few doubt his presence and input will be felt.
In New York, Cardinal Edward Egan issued a letter to parishioners, apologizing "if in hindsight" he has made any mistakes in handling sex abuse cases involving priests.
"I will do everything in my power to ensure, as much as is humanly possible, that such abuse by clergy will never happen again," Egan wrote in the letter, which was read at Masses throughout the weekend. "You should expect nothing less of me, and the leaders of our church."
Miami Archbishop John C. Favalora assured Miami-Dade and Broward County parishioners Sunday that there is no active priest in the archdiocese who is the subject of a credible allegation of sexual misconduct.
"To those who have been offended by a priest and to their families and all who love them, I express sincere sorrow of the church and my firm resolution to do all that is possible to prevent such offenses from happening in the Archdiocese of Miami," Favalora said in a videotaped message.
In a letter from Bishop Thomas Daily, parishioners in the Diocese of Brooklyn were told the names of 21 priests, stretching back some 20 years, were given to the district attorney's office of Brooklyn and Queens counties.
Boston became the epicenter of the sexual abuse controversy in January, when published reports disclosed that Law and other church leaders had simply reassigned a priest accused of pedophilia to another parish.
The aftershocks of these revelations have since been felt in parishes throughout the country as additional reports of abuse and coverups have come to light.
The spotlight returned to Boston in recent weeks following new revelations about a priest who was allowed to continue leading local parishes despite his endorsement of sex between men and boys.
The release of Rev. Paul Shanley's damaging personnel records heightened the intensity of the national debate and escalated calls for Law's resignation. Ten days ago, in a letter to his "brother priests," Law said he would continue leading the Boston archdiocese "as long as God gives me the opportunity."
For the first time, the weekly protesters at the Cathedral were confronted by a vocal group of sign-carrying Law supporters. The mainly Hispanic group stood on the steps, directly across from the protesters, and at least momentarily drowned out the angry shouting with their songs.
One carried a sign saying, "The good shepherd does not abandon his flock."
Other parishioners spoke out in support of the cardinal — and his message — after the service.
"He made a very moving statement about what has happened and the reform that no doubt will occur," said Mary Butler of Quincy. "I certainly think the church will emerge much stronger because of this."