"My resignation is not part of the solution as I see it," he told a group of about 520 Boston-area priests gathered for a conference at the Boston Park Plaza Hotel. "I want the archdiocese to become a model for how this issue should be handled. I have a responsibility as your archbishop to help that happen, and I want you to know that with every fiber of my being I am going to try and see that that happens."

Law also said he would draft a letter to area Catholics about clergy misconduct and instruct priests to read the letter at Mass in all archdiocesan parishes.

"I wish it were possible to go back in time and undo some of the decisions that I made," he said. "I now see that these were wrong decisions ... While I, and those associated with me, attempted to do our best in responding to these cases in the past, that effort, as I now see it, was flawed."

Law's speech was closed to reporters, and the cardinal would not speak to the news media yesterday. But the archdiocese arranged for two priests loyal to Law to brief reporters, and at 9:30 last night, about seven hours after the cardinal spoke and several hours after the evening television newscasts, the archdiocese released seven sentences from Law's remarks.

"What I have come to learn with a much more vivid clarity during the past weeks is that our singular focus must be the protection of children," Law said.

Only one archbishop has ever been forced to quit over the issue of clergy sexual misconduct: In October, the pope forced the resignation of John Aloysius Ward, the archbishop of Cardiff, Wales, for allegedly ignoring warnings about two priests who were later convicted of child abuse.

Law's own future became the subject of much speculation after he acknowledged in a court filing in June that he knew John J. Geoghan was a child molester before reassigning him, based on medical advice, to a new parish in 1984. In the last two weeks, after Law called his handling of the case "in retrospect ... tragically incorrect," a Boston Globe columnist, Derrick Z. Jackson, as well as a member of the Knights of Malta, a Catholic fraternal organization, writing in the Wall Street Journal, have called for Law's resignation. So have some Catholic laypeople interviewed by reporters.

But priests yesterday greeted Law's announcement that he would not resign with applause.

"Cardinal Law is the best thing that's ever happened to the church of Boston in terms of leadership," said Monsignor Paul B. McInerny, a longtime Law aide who now serves as director of Boston Catholic Television. "There has not been, from my perspective, a bishop who has been more gifted, more pastoral, more committed, more generous, more compassionate -- all of the things a good priest should be, Bernard Cardinal Law is an exemplary model of that. ... This one mistake ... is not the reason and cannot be the thing that ends his incredible leadership of this local church."

Several other priests interviewed before the conference said they also do not believe Law should resign.

"If he were to go now, it would be walking away in the middle of a difficult time, and I can't imagine Rome would have him go now," said the Rev. Walter H. Cuenin, pastor of Our Lady Help of Christians Church in Newton. "Even guys who may not be that supportive of the cardinal feel bad for him in a human sense and want to support him."

Monsignor Frederick J. Murphy, rector of the Cathedral of the Holy Cross in the South End, also said he would oppose Law's resignation.

"He's not going to have an easy time for the next few weeks and months -- he's right on the firing line," Murphy said. "But we pray for him all the more now. I feel for him, and I hope people bear in mind the wonderful things he's done."

The Rev. Robert W. Bullock, pastor of Our Lady of Sorrows Church in Sharon, said he too would not support the cardinal's resignation. And he argued that the focus on the cardinal ignores the responsibility of other church officials for mishandling the issue of clergy sexual abuse.

"It isn't just the cardinal; it's the way we operate. There are structural issues," Bullock said. "What is it that has made us priests be so supine, and unwilling to stand up and take risks? To speak out when something awful is happening, and not to cover up? To name things for what they are? The leadership has not protected children, and we have not protected children."

Law, 70, has been the archbishop of Boston since 1984, and will be required under current church policy to offer his retirement at the age of 75. In an interview Nov. 1, after he became a defendant in the Geoghan civil cases, Law said the Vatican had not criticized him for his handling of the matter and had not asked him to resign. He said at that time that he expected to remain in Boston for the rest of his career.

Geoghan was convicted on Friday of one count of indecent assault, and yesterday a judge ordered the former priest, who Law had defrocked in 1998, to undergo a monthlong psychiatric evaluation at Bridgewater State Hospital before being sentenced.

Although Law has called the issue of clergy sexual abuse "a matter of open and public discussion," many priests refused to speak to reporters at the hotel yesterday. Most did not wear clerical collars -- they said they were instructed to dress casually weeks ago -- and one was seen hastily removing his collar as he neared reporters.

One priest, asked by a reporter how he was doing, snapped, "Better than you."

Outside the hotel stood a lone protester, Steve Lynch of Danvers, who says he was molested by a priest when he was an altar boy in 1968. Lynch, 42, shouted at the cardinal as he entered the hotel, saying "I want the truth, Bernard Law."