(AP) -- Britain's Prince William and his wife, Kate, paid their respects with a handwritten note Tuesday at the Sept. 11 museum and told its leaders they were struck by the enormity of the loss in the 2001 terror attacks.

"In sorrowful memory of those who died on 11th September and in admiration of the courage shown to rebuild -- William and Catherine," she wrote in a note the couple left with flowers on the memorial pools lined with the names of the nearly 3,000 victims.

Making their first visit to New York, the Duke and Duchess of Cambridge visited its most somber site amid a three-day agenda filled with events linked to their charitable interests in conservation and youth development, receptions with actors and others in creative and technology fields, and a bit of all-American entertainment -- a pro basketball game.

As the royals toured the museum devoted to the attacks, they examined such artifacts as preserved trident columns from one of the fallen twin towers' facades and viewed rows upon rows of victims' portraits. Like other visitors, they left virtual signatures to be projected on a crucial underground wall that survived the attacks and held back the Hudson River, with Kate looking on with a smile as hers appeared. And they asked questions about the memorial pools' design, about how victims' families had responded to the museum, and about the attacks themselves, National Sept. 11 Memorial and Museum President Joe Daniels said.

"You could see in, really, both of their eyes, the sort of care and curiosity they had for the story of what happened and the people who died that day," Daniels said.

William remarked on "how much people understand and need to understand how impactful the scale of loss was" on American history, Daniels said.

Kate noted the enormity of the museum's space, which stretches seven stories belowground amid the fallen towers' footprints, and "talked about how moving the memorial was and being able to touch the names of the victims," museum chief of staff Allison Blais said.

Curious museumgoers stood by to get a look at the royals -- including the pregnant Kate's hot-pink Mulberry coat, black tights, and black stiletto-heeled pumps, over a black dress from maternity designer Seraphine. Other fans braved heavy, cold rain outside. Krupa Shah took a vacation day from her Manhattan finance job.

"I took the day off work when they got married. I didn't go to a family event when Kate was in labor, because I wanted to know what she had," the New Jersey resident said.

The royals, now 32, were beginning their studies at the University of St. Andrews when the attacks happened. Sixty-seven British citizens died that day, the highest toll of any country other than the U.S.

After the museum, the royal couple watched dance and storytelling performances at The Door, a youth development organization. Tapping his feet quietly during a hip-hop-style dance performance, William also showed he was moved by one young man's story of his father's incarceration and his own brush with a jail term in an assault case.

"I had a low period in my life, and never in a million years did I expect I would be performing for the duke and duchess," Steven Prescod, 22, said later.

William approached Prescod and peer educator Ely Olivero, 22, after the show, calling it "incredible," Olivero said.

The royals went on to a reception celebrating the arts, with guests including actor Patrick Stewart and producers Harvey Weinstein. William met New York Mayor Bill de Blasio at a reception at the Empire State Building focusing on innovation. The rain stopped just before William and de Blasio stepped out on the skyscraper's 86th-floor observation deck.

"Wow, this is great!" William remarked to de Blasio.

Finally, the duke and duchess were expected Tuesday night at a black-tie fundraiser for their alma mater St. Andrews.

On Monday, William met with President Barack Obama at to the White House and spoke at a World Bank conference. Kate wrapped Christmas gifts and helped children decorate picture frames while touring a child development center. Both royals later attended a reception with former Secretary of State Hillary Rodham Clinton, Chelsea Clinton and her husband, Marc Mezvinsky.

William and Kate then took in a Cleveland Cavaliers-Brooklyn Nets game, meeting music power couple Jay-Z and Beyonce and Cavaliers star LeBron James.