Only American cardinals have been called to Rome
He told American cardinals there was no place in the Roman Catholic Church for priests who sexually abused children.
"The abuse which has caused this crisis is by every standard wrong and rightly considered a crime by society; it is also an appalling sin in the eyes of God," said the Pope in his address, the text of which was released by the Vatican.
He added that a "generalised lack of knowledge of the nature of the problem, and also at times the advice of clinical experts, led bishops to make decisions which subsequent events showed to be wrong".
The 81-year-old pontiff also said that the "immense spiritual and social good" of a vast majority of priests in the United States should not be forgotten.
The growing number of cases of sexual abuse of minors by American Catholic priests - both alleged cases and those which have led to criminal convictions - has spurred calls for drastic action.
After the initial meeting, Bishop Wilton Gregory told a press conference that the cardinals had a clear task ahead of them: "We must assure our people that we will not place their children in harm's way."
Growing alarm
Although sex abuse scandals have rocked dioceses in other nations, only the American cardinals have been called to the Vatican.
America's most senior cardinal, Boston's Archbishop Bernard Law, is under pressure after acknowledging that he transferred a priest to another parish despite knowing of sexual misconduct allegations against him.
One unnamed US cardinal told The Los Angeles Times that he and other prelates planned to urge the Vatican to ask Cardinal Law to resign.
Before the address by the Pope, the cardinals met him for informal talks. They will also hold formal talks with Vatican officials in charge of priests and bishops worldwide, including Cardinal Joseph Ratzinger, who is in overall charge of doctrinal discipline in the church.
Financial burden
More than 400 complaints have been lodged against priests in the Boston diocese alone.
And accusations of child molestation have been made in at least 16 other US dioceses including Chicago, New York, Philadelphia and San Francisco.
The scandals are also a huge financial burden for the Church and there is talk that some archdioceses will be bankrupted as a result.
Although the US church is the hardest hit by sex abuse allegations, similar scandals have hit clergy in different countries in recent years, including Austria, Ireland, Poland, France and Mexico.