Obama told an audience of victims' relatives, survivors, first responders and people who worked on the cleanup that it was an "honor for us to join in your memories, to recall and to reflect, but above all to reaffirm the true spirit of 9/11 -- love, compassion, sacrifice -- and to enshrine it forever in the heart of our nation."
"All who come here will find it to be a profound and moving experience," he added.
Obama, who toured the museum shortly before the ceremony began, singled out the story of 24-year-old Welles Crowther, who worked in the south tower on Sept. 11. Crowther is said to have been spotted helping people out of the building, before going back up to rescue more, while wearing a red bandanna over his face. He died when the tower collapsed, and his body was found six months later.
A bandanna belonging to Crowther is displayed in the museum.
Obama introduced his mother, Alison Crowther, who said "it is our greatest hope that when people come here and see Welles' red bandanna they will remember how people helped each other that day."
Other stories of survivors and victims were told at the ceremony Thursday. Speakers recalled the pain and triumph of the day, and said the museum was built to preserve those stories. Members of the audience wept and wiped their eyes throughout the program.
The museum at ground zero, in what was the World Trade Center basement, leads people on an unsettling journey through the terrorist attacks, with forays into their lead up and legacy.
There are scenes of horror, including videos of the skyscrapers collapsing and people falling from them -- one of several areas of the museum that are tucked away in alcoves, behind posted warnings. The museum also has what it calls "early exits," where visitors can leave if they get overwhelmed. But there also are those symbols of heroism, like the bandanna, damaged fire trucks and the wristwatch of one of the airline passengers who confronted the hijackers.
Florence Jones donated the shoes she was wearing on Sept. 11 -- which she took off on the 60th floor as she made her way out of the tower.
"I wanted my nieces and my nephew and every person that asked what happened to see them and maybe understand a little bit better what it felt like to be us on that day," she said at the ceremony.
Visitors to the museum start in an airy pavilion where the rusted tops of two of the World Trade Center's trident-shaped columns shoot upward. From there, museumgoers descend stairs and ramps, passing through a dark corridor filled with the voices of people remembering the day and past the battered "survivors' staircase" that hundreds used to escape the burning towers.
At the base level — 70 feet below ground, amid remnants of the skyscrapers' foundations — there are such artifacts as a mangled piece of the antenna from atop the trade center and a fire truck with its cab shorn off.
Then, galleries plunge visitors into the chaos of Sept. 11: fragments of planes, a set of keys to the trade center, a teddy bear left at the impromptu memorials that arose after the attacks, the dust-covered shoes of those who fled the skyscrapers' collapse, emergency radio transmissions and office workers calling loved ones, even a recording of an astronaut solemnly describing the smoke plume from the International Space Station.
Sprinkled in are snippets about the 19 hijackers, including photos of them on an inconspicuous panel.