Benedict was answering questions that were submitted in advance by reporters aboard a special Alitalia airliner as he was flying from Rome to Washington to begin his first papal pilgrimage to the United States.
"It is a great suffering for the Church in the United States and for the Church in general and for me personally that this could happen," the pope said.
"It is difficult for me to understand how it was possible that priests betray in this way their mission ... to these children. "I am deeply ashamed and we will do what is possible so this cannot happen again in the future", the pope said.
Benedict pledged that paedophiles would not be priests in the Roman Catholic Church.
"We will absolutely exclude paedophiles from the sacred ministry," he said, speaking in English.
"It is more important to have good priests than many priests. We will do everything possible to heal this wound."
But The Age quotes a former Benedictine priest who said the remarks were too little, too late, and a support group for victims of predator priests dismissed them as meaningless.
"It's a great public relations statement, but it's 25 years too late," Patrick Wall, who left the church 10 years ago over the child sex scandal, told AFP.
"As chief enforcer for the Congregation of the Doctrine of the Faith for 24 years, he had the power and the jurisdiction to stop this, but he did nothing," Wall said.
"He needs to have the power and the moral fortitude to take the bishops, priests and deacons who offend against children out of ministry."
The largest group of victims of predator priests, the Survivors Network for those Abused by Priests (SNAP), called for strong actions, not mere words, from the pope.
"Yesterday, a list was released of 19 bishops who offended against children who have never been removed from ministry," said one priest.
"There were 51 new credible child molestation accusations against priests and bishops in the US last year. The conflict is continuing," he said.
Upon his arrival later at Andrew Air Force base, President George W. Bush greeted the pope.
But before leaving the Vatican, Pope Benedict also issued a message in which he urged nations to slash military spending and channel savings into peaceful development projects around the world, Total Catholic reports. He also called on governments to halt the spread of handguns and other small-calibre weapons "that fuel local wars and urban violence and unfortunately kill too many people across the world every day".
The Pope made his comments in a written message presented to participants gathered for an April 11-12 seminar sponsored by the Pontifical Council for Justice and Peace.
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