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Pope Benedict XVI stepped onto U.S. soil for the time as pontiff Tuesday, arriving to a presidential handshake and wild cheering only hours after he admitted that he is "deeply ashamed" of the clergy sex abuse scandal that has devastated the American church.

Benedict gave hundreds of spectators a two-handed wave as he stepped off a special Alitalia airliner that brought him from Rome. Students from a local Catholic school screamed ecstatically when they saw the pope, who shook hands warmly with President Bush, first lady Laura Bush and their daughter Jenna on the tarmac.

Hundreds of onlookers, some from local Roman Catholic parishes, clapped and shouted as they watched the scene from nearby bleachers.

• PHOTOS: Past Popes and Presidents | Pope Embarks on Historic U.S. Visit

Benedict tackled the most painful issue facing the U.S. Catholic Church — clergy sex abuse — on his flight to America. The U.S. church has paid out $2 billion in abuse costs since 1950, most of that in just the last six years.

Seemingly in a nod to his American flock, the pope spoke in English as he answered questions submitted in advance by reporters.

"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," Benedict 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.

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Benedict pledged that pedophiles would not be priests in the Catholic Church.

"I do not wish to talk at this moment about homosexuality, but about pedophilia, which is another thing," he said.

"We will absolutely exclude pedophiles from the sacred ministry. It is more important to have good priests than many priests. We will do everything possible to heal this wound."

Click to read about a U.S. Muslim group that declined to meet with the pope.

Gary Bergeron, who was molested by a priest in the 1970s in Lowell, Mass., called the comments a "step I've been looking for." Bergeron said he was disappointed that Benedict did not plan to visit the Archdiocese of Boston, the scene of a case that sparked the greater scandal, but urged the pontiff to meet with victims this week.

The pope's promise failed to mollify other advocates for abuse victims, however. They said the problem is not just molester priests, but bishops and other church authorities who have let errant clergymen continue to serve even after repeated allegations.

"It's easy and tempting to continually focus on the pedophile priests themselves," said Peter Isely, a board member of the Survivors Network of those Abused by Priests. "It's harder but crucial to focus on the broader problem — complicity in the rest of the church hierarchy."

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Benedict's pilgrimage is the first trip by a pontiff to the United States since the Boston case in 2002 triggered a crisis that spread throughout the United States and beyond. Hundreds of new charges — many dating back decades — have surfaced each year since. There were 691 new accusations in 2007 alone, according to an annual report from the U.S. Conference of Catholic Bishops.

As head of the Vatican agency that enforces adherence to Catholic doctrine, then-Cardinal Joseph Ratzinger was heavily involved in gaining Vatican approval for the reforms U.S. bishops proposed for the American church. The bishops have since released several reports analyzing the scandal and have pledged that all credibly accused priests will be pulled from public ministry.

Benedict described his pilgrimage as a journey to meet a "great people and a great church." He spoke about the American model of religious values within a system of separation of church and state.

Click to view the itinerary of Pope Benedict XVI's U.S. trip

President Bush made the unusual gesture of greeting Benedict at Andrews Air Force Base — the first time he has welcomed a foreign leader there. The two will meet again Wednesday, when a crowd of 9,000 or more is expected at the White House to greet Benedict on his 81st birthday.

Aides say he is in good health and the pope seemed spry as he stepped energetically off the plane Tuesday.

Benedict said he will discuss immigration with Bush, including the difficulties of families who are separated by immigration.

While the pope and Bush differ on such major issues on the Iraq war, capital punishment and the U.S. embargo against Cuba, they do find common ground in opposing abortion, gay marriage and embryonic stem cell research.

White House press secretary Dana Perino said she wouldn't rule out the sex abuse being discussed between the pope and the president, but added that it's not necessarily one of Bush's top priorities in his meeting with Benedict.

Perino said the two leaders would likely discuss human rights, religious tolerance and the fight against violent extremism. She downplayed their differences over Iraq.

Benedict "will hear from the president that America and the world need to hear his message, that God is love, that human life is sacred, that we all must be guided by common moral law, and that we have responsibilities to care for our brothers and sisters in need, at home and across the world," Perino said.

After making little headway in his efforts to rekindle the faith in his native Europe, the German-born Benedict is visiting a country where many of the 65 million Catholics are eager to hear what he says and get to know him. A poll released Sunday by the Center for Applied Research in the Apostolate at Georgetown University found eight in 10 Catholics are somewhat or very satisfied with his leadership.

Benedict is scheduled to visit U.N. headquarters on Friday to meet with Secretary-General Ban Ki-moon and to address the General Assembly.

Ban said he is looking forward to a wide-ranging discussion with the pontiff on issues ranging from climate change and fighting poverty to disarmament and promoting cultural dialogue.

"We are now facing many challenges these days," Ban told reporters. "We need really strong spiritual support from the pope."

The pope's visit will be the fourth by a leader of the Roman Catholic church to the United Nations: Paul VI came in 1965 when the U.N. celebrated its 20th anniversary; John Paul II came in 1979 at the start of his pontificate and again in 1995 for the U.N.'s 50th anniversary.