The president closed his eyes and clasped his hands at the outdoor memorial where the twin towers of the World Trade Center once dominated the Manhattan skyline. He shook hands with Sept. 11 family members and others dressed in black at the site where their daily work and said they had a president who has “got your back.”

Former New York Mayor Rudy Giuliani, who led the city in dark days after the attacks, joined Obama during the day.

At the Pentagon, meanwhile, Vice President Joe Biden led a similar wreath-laying ceremony at the site where another hijacked plane crashed into the nation’s military headquarters.

Obama’s visit to New York came as new details emerged of the daring raid on Bin Laden’s Pakistan compound early Monday local time. A senior defense official said Thursday that only one of the five people killed in the raid was armed and fired a shot — an account that differs from original administration portrayals of an intense firefight.

The White House also now says Bin Laden was unarmed when he was shot, after officials initially said the terrorist was holding a gun or even firing.

Obama’s New York visit was intended to have a measured tone — not a bookend to President George W. Bush’s visit after the attacks when Bush took a bullhorn and called out his defiance to the terrorists.

Obama spokesman Jay Carney told reporters traveling with the president on Air Force One that the trip was intended in part “to perhaps help New Yorkers and Americans everywhere to achieve a sense of closure with the death of Osama Bin Laden.”

Obama invited Bush to join him Thursday, but the former president declined.

The president sought to handle the moment without being seen as overly celebrating Bin Laden’s death or aiming to boost his own standing.

Al-Qaeda terrorists hijacked jets and flew two of them into the World Trade Center’s towers. Both buildings collapsed, trapping thousands inside and also claiming the lives of firefighters and others who had rushed to help. A third plane slammed into the Pentagon. Officials have speculated that a fourth plane had been heading for the US Capitol or perhaps even the White House when it crashed after passengers fought back in Pennsylvania.

The bustling construction site that Obama visited bears little resemblance to the pit that remained after the rubble of the towers was removed. The emerging skyscraper informally known as Freedom Tower is more than 60 stories high now. Mammoth fountains and reflecting pools mark the footprints of the fallen twin towers.

Jim Riches, whose firefighter son was among the nearly 3,000 people killed at the World Trade Center, planned to meet with the president on Thursday.

“I just want to thank him, hug him and thank him and shake his hand,” Riches said. “Father to father. Thank you for doing this for me.”

Obama arrived in New York City Thursday after rejecting calls to release photos of a slain Bin Laden so the world could see some proof of death. The president said he would not risk giving propaganda to extremists or gloat by publicizing grotesque photos of a terrorist leader shot in the head.

To those who keep on doubting, Obama said, “You will not see Bin Laden walking on this earth again.”