During Thursday's open-air Mass, the Pontiff said: "No words of mine can describe the pain and the harm inflicted by the sexual abuse of minors.
"It is important that those who have suffered be given loving pastoral attention. Nor can I adequately describe the damage that has occurred within the community of the Church."
Efforts to protect children must continue, he said.
For the third time in as many days, he has done what many Catholics have been asking for years - he has condemned and publicly accepted full responsibility for the crimes of sexual abuse committed by Catholic priests in the United States, says the BBC's David Willey who is travelling with the Pope during his visit.
Many members of the congregation were immigrants from various countries in central and South America and they cheered the Pope wildly when he added some remarks in fluent Spanish, praising the vitality of their Christian faith.
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Pope walking through crowd
Before Pope Benedict arrived here, polls showed that many Americans knew little or nothing about him.
Those who have watched him so far have found a German-born Pope who speaks excellent English, appears vigorous for his 81 years, and displays a keen sense of many of the critical issues facing his 65-million-member American flock, our correspondent adds.
Gates at the Washington sports stadium opened before dawn to allow people to trickle through stringent security measures ahead of the Mass at 1000 (1400 GMT).
Among the first to arrive was Barbara Loh, who told the Associated Press agency: "I've been Catholic all my life and... my dream has always been to see the Pope."
Controversial meeting
On Wednesday, the pontiff met President George W Bush at the White House.
Speaking later to bishops, he criticised their handling of child sex scandals that have rocked the Roman Catholic Church in the US.
After the Mass, the Pope is due to meet leaders from other faiths at the Pope John Paul II Cultural Centre in Washington.
That gathering has attracted controversy.
Sikhs have refused to attend after the secret service insisted ceremonial daggers be removed.
One Muslim group has also pulled out, saying the Pope's statements have given the impression that he is intolerant of Islam.
Other Muslim leaders said they were attending out of respect for the Catholic Church, but admitted they too had some concerns.
Muslims around the world were upset when the Pope in 2006 quoted a medieval text that said Islam was violent.
Relations were upset again when the Pope baptised an Egyptian Muslim known to be a fierce critic of Islam at a high-profile ceremony in the Vatican on the Easter weekend.
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