Pope Benedict XVI will arrive in New York Friday for the final leg of a trip to America in which he has been working to heal damage caused by the sexual abuse scandal and address what he called a crisis of truth and faith in Catholic education.

Yesterday, he expressed sorrow for problems he called divisive and harmful, but called repeatedly for his flock to embrace hope and the church, and to become more Catholic, not less.

“Who can deny that the present moment is a crossroads, not only for the church in America but also for society as a whole?” he said yesterday at the Nationals Park Stadium in Washington, D.C., where about 46,000 gathered under the bright sun to celebrate Mass.

“The challenges confronting us require a comprehensive and sound instruction in the truths of the faith. But they also call for cultivating a mindset, an intellectual ‘culture,’ which is genuinely Catholic, confident in the profound harmony of faith and reason, and prepared to bring the richness of faith’s vision to bear on the urgent issues which affect the future of American society,” Benedict said.

He laid out some of those challenges earlier in the week. On Wednesday, he called on church members to avoid the press of secularism and to stay true to the church’s social values, including its stances against abortion and divorce. Yesterday, he focused more on the sex abuse scandal and schools.

In the afternoon, he and Sean Cardinal O’Malley of Boston — the epicenter of the priest abuse scandal — met privately with a small group of victims and prayed with them.

The meeting and his words on the sexual abuse of minors by Catholic priests seemed to soothe some of the most vocal critics of the church’s handling of the crisis.

Addressing the topic for the third time on his trip, he said during the stadium Mass: “It is in the context of this hope born of God’s love and fidelity that I acknowledge the pain which the church in America has experienced as a result of the sexual abuse of minors. No words of mine could describe the pain and harm inflicted by such abuse.”

A statement released by a Catholic group that was created in the wake of the scandal and has been highly critical of the Catholic hierarchy, Voice of the Faithful, said it welcomed Benedict’s acknowledgement of the abuse even while calling for a shakeup of the church hierarchy.

One of Benedict’s strongest messages yesterday was for Catholic educators at a gathering at the Catholic University of America that included representatives from all of the archdioceses, which run parochial schools, and 200 presidents of Catholic universities and colleges. In particular, he singled out faculty at Catholic colleges and universities, among whom there has been an ongoing debate about the role of Catholic culture and moral values.

“In virtue of this freedom you are called to search for the truth wherever careful analysis of evidence leads you. Yet it is also the case that any appeal to the principle of academic freedom in order to justify positions that contradict the faith and the teaching of the Church would obstruct or even betray the university’s identity and mission,” Benedict said.

The Catholic culture and moral values taught at Catholic universities and parochial schools, he argued, are what continues to make them unique and relevant alongside America’s public education system.

His comments seemed to put him squarely on the side of Catholic conservatives who have criticized some schools for such acts as allowing gay and lesbian groups on campus and inviting pro-choice commencement speakers. Benedict also had praise for Catholic schools, which he said have been instrumental in educating those who have been “neglected,” including African Americans, Native Americans, and immigrants.

He also indirectly acknowledged the enrollment crisis currently facing Catholic schools in the younger grades. Catholic school enrollment has dropped by more than half since 1960, according to a 2007 report by Education Next, a publication of the Hoover Institution. Another report released ahead of the pope’s visit by the Thomas B. Fordham Foundation projected that nearly all inner-city Catholic schools were likely to close by 2018.

“Their long-term sustainability must be assured,” Benedict said of parochial schools, closing his speech with a “special appeal” to religious brothers, sisters, and priests.

“Do not abandon the school apostolate; indeed, renew your commitment to schools especially those in poorer areas,” he said.

He continued the theme at a meeting with interfaith leaders at the Pope John Paul II Cultural Center yesterday evening, praising faith-based schools in general as a way for “young people to learn to respect the beliefs and practices of others, thus enhancing a nation’s civic life.”

Benedict also pointed to positive signs for the Church, among them the growth in membership spurred by Hispanic members. For the first time, he thanked them directly yesterday — in Spanish — for their participation in the church.

“Don’t be conquered by pessimism, inertia or problems,” he said. The church, he continued, “has been growing thanks to the vitality of the testimony of the Spanish-speaking faithful.”