"Multilateral consensus," he said, speaking in French, "continues to be in crisis because it is still subordinated to the decisions of a small number."
The world's problems call for collective interventions by the international community, he said.
"The promotion of human rights remains the most effective strategy for eliminating inequalities between countries and social groups, and increasing security," the pope said.
Benedict, only the third pope to address the United Nations, made the remarks after three dramatic days in which he repeatedly discussed America's clergy sexual abuse scandal.
The U.N. setting contrasted dramatically with the intimacy of a meeting Thursday, at which Benedict prayed with weeping victims of childhood sexual abuse by priests.
The pope took an early morning flight from the nation's capital to New York City. He was greeted by New York Cardinal Edward Egan and taken to a helicopter for the ride into Manhattan.
The Rev. Federico Lombardi, a papal spokesman, said that Benedict and Boston Cardinal Sean O'Malley met with a group of five or six abuse victims for about 25 minutes, offering them encouragement and hope. The group from O'Malley's archdiocese were all adults, men and women, who had been molested when they were minors. Each spoke privately with the pope and the whole group prayed together.
One of the victims, Bernie McDaid, told The Associated Press that he shook the pope's hand, told him he was an altar boy and had been abused by a priest in the sacristy of his parish. The abuse, he told Benedict, was not only sexual but spiritual.
"I said, 'Holy Father, you need to know you have a cancer in your flock and I hope you will do something for this problem; you have to fix this,"' McDaid said. "He looked down at the floor and back at me, like, 'I know what you mean.' He took it in emotionally. We looked eye to eye."
Olan Horne, another Boston-area victim who prayed and talked with Benedict, told the AP, "I believe we turned the pope's head a little in the right direction."
Both men have worked with church officials in the aftermath of the crisis, and met with a new office established by U.S. bishops in response to the scandal.
Their sentiments were echoed by O'Malley, who called the meeting "a very moving experience for all who participated."
Benedict's address to the presidents of Catholic colleges and universities was among the most anticipated of his trip, but was overshadowed by the meeting with victims.
The pope, a former academic, said academic freedom has "great value" for the schools, but does not justify promoting positions that violate the Catholic faith.