A handwritten message on the flowers said: "In sorrowful memory of those who died on 11th September, and in admiration of the courage shown to rebuild." Each had signed their names, William and Catherine, underneath the message.
The couple arrived at the World Trade Center site in lashing rain, the Duchess wearing a fuchsia-coloured coat by Mulberry over a Seraphina maternity dress.
Before placing their flowers, the couple were told about the building of the memorial, which features two reflecting pools covering the footprint of the two towers brought down by terrorists in 2001.
The Duke and Duchess placed their bouquet at the spot where the names of the 40 passengers and crew of United Flight 93, which crashed in Pennsylvania on 9/11, are inscribed. Royal aides said the location was chosen by the New York Port Authority, which owns the site.
Then they were taken inside the museum, where they wrote their electronic signatures next to a piece of steel recovered from the wreckage.
Allison Blais, the museum's chief of staff, said the Duchess "talked about how in awe she was of the enormity of the space. It was something she did not anticipate. She also talked about how moving the memorial was, and being able to touch the names of the victims outside on the pools."
Joe Daniels, the museum's chief executive and president, said: "You could see it really in both their eyes, the sort of care and curiosity they had for the story of what happened and the people who died that day." He said one of the most moving moments was when they visited the In Memoriam room, where photographs of nearly all of the victims line the walls.
As the couple gazed at the pictures of the dead, outside recorded voices intoned the names of their friends and loved ones: "My beloved husband ... my best friend ... my beloved daughter."
The victims of 9/11 included 67 Britons, whose names are among those carved into the bronze around the pools.
In an inner room the Duke and Duchess heard the history of one of the victims, John Katsimatides, in which his sister spoke of his love of dancing and how much he loved life. "They seemed quite struck by that," said Mr Daniels.
As they entered the museum the couple passed two massive steel columns recovered from the wreckage. On the side of them could be seen the word "SAVE" spray-painted by a recovery worker signalling it should be kept for posterity.
In the Memorial Hall, at the bedrock level seven storeys below ground, they saw an artwork made of 2,983 blue squares created by the artist Spencer Finch. Each tile was in a different shade of blue, evoking the sky that day.
A quote from the poet Virgil, made from reforged steel from the World Trade Center, says: "No day shall erase you from the memory of time."
The Duke and Duchess met LeBron James, the basketball star, in New York on Monday night, and were taken by surprise when James put his arm around the Duchess in what observers suggested was against royal protocol. They had attended a game between the Brooklyn Nets and the Cleveland Cavaliers. The Palace denied it broke any protocol.
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LeBron James' embrace has sparked criticism in the British press. Photo / AP