Pope John Paul II and Bishop James R. Crumley Jr. of the Lutheran Church in America made public yesterday a historic exchange of personal letters pledging renewed efforts to repair, by the turn of the century, the 465-year-old schism that opened the flood gates of the Protestant Reformation.

The letters, released simultaneously at the Vatican and at Lutheran headquarters in New York, are the first public exchange between a pope and the head of a Protestant church, at least in modern times. They follow 20 years of scholarly dialogues between teams of theologians from both churches and three personal conversations between the two church leaders.

Progress has been made to unite the churches again, the pope wrote, but "we still experience anguish because full unity has not yet been achieved."

He added that it "is my prayer" to make "the dawn of the third millennium the beginning of a special time for seeking full unity in Christ."

The letters mark a high point in relations between churches that have long been bitter theological opponents. Only a generation ago, many Lutheran preachers were relentlessly anti-Catholic, and Catholic scholars published harsh attacks on all of Protestantism, which was born in the Reformation.

The pontiff's letter, dated July 22, was in a response to a May 22 letter from Crumley, in which he reviewed areas of Catholic-Lutheran cooperation and theological agreement that have been arrived at in the last 20 years.

" . . . . But the relationship remains fragile," the Lutheran said. "Therefore I am anxious for us to write a word of encouragement to each other to persevere in the difficult task of expressing our unity."

Ever since the Second Vatican Council, a quarter-century ago, acknowledged non-Catholic Christians as "separated brethren" instead of calling them anathema, teams of scholars have been searching out the areas of agreement.

The Catholic-Lutheran talks have produced substantial agreements on such key questions as the meaning of baptism, of the eucharist (Holy Communion) and how a person may be saved. The biggest stumbling blocks that remain, Crumley said yesterday in a telephone interview, involve the validity of one another's ministry, papal primacy and "how much diversity can be acceptable to the two churches."

Although the theological dialogues are conducted by an international team of scholars from the two churches, yesterday's exchange on the Lutheran side involved only the Lutheran Church in America. The American church made the breakthrough, Crumley said, because in the United States "we do not have the acrimonious history" that exists in some part of the world.

A public service celebrating the progress will be held at Reformation Lutheran Church on Capitol Hill Nov. 14, while the nation's Roman Catholic bishops are in town for their annual meeting. Both Catholic and Lutheran bishops will take part in the service.

Events such as the joint worship service and the public exchange of letters are important for symbolic reasons, Bishop James W. Malone of Youngstown, Ohio, president of the National Conference of Catholic Bishops, said yesterday. "It's almost like a love affair. Two people care for each other, are committed to each other, but it's important to give evidence of that by certain signs and symbols."

After some stunning breakthroughs in the early years of church unity efforts encouraged by Popes John XXIII and Paul VI, enthusiasm waned and the present pontiff has been perceived as putting a low priority on ecumenism.

That's why the papal letter released yesterday is "very important," Crumley said. "It is especially important to have an explicit statement from the pope about his commitment to ecumenism since in several places this is doubted."

Besides, he observed wryly, the last letter a pope wrote to a Lutheran was Leo X's 1520 bull of excommunication and anathema to Martin Luther.