June Pollicino, who lost her husband on 9/11, said: “I feel much more relaxed. After the ninth anniversary, those next days it started building up to the 10th anniversary. This year it’s different in that regard. It’s another anniversary we can celebrate in a discreet way.”

The day’s main event was the ritual reading of names – 2,983 in all, including the 9/11 victims and those killed in the precursor to those attacks, the 1993 car bombing of the World Trade Centre.

The reading paused for silence at the exact time each of the four planes hijacked by al-Qaeda turned into fireballs – two smashing into the Twin Towers, one into the Pentagon and one into a Pennsylvania field.

Another two moments of silence were to be observed at the times the two main towers of the World Trade Centre collapsed, accounting for the vast majority of 9/11’s dead.

The ceremony took place on the grounds of the 9/11 Memorial between the two huge black fountains that mark the footprints of the old Twin Towers.

Obama and his wife Michelle were observing the anniversary with a moment of silence outside the White House, then a visit to the Pentagon memorial.

Vice-President Joe Biden, meanwhile, was travelling to Shanksville, Pennsylvania, where United flight 93 crashed after passengers attacked the hijackers and prevented them from hitting another presumed high-profile target, such as the US Capitol building.

The White House said Obama had been briefed by “key national security principals on... preparedness and security posture” for the anniversary.

But in keeping with the lower key atmosphere this year, there was no official suspension of the bitter presidential campaign.

Former president Bill Clinton was campaigning for Obama and speaking out against Republican Mitt Romney at an event in Miami. Romney issued a statement thanking US troops and saying “those who would attack us should know that we are united”.

The passage of time appears to have cooled public attention to September 11, particularly in contrast to the huge media coverage of the 10th anniversary, which many saw as a suitable moment for allowing commemorations to peak.

A new skyscraper at One World Trade Centre is near completion and is officially the tallest building in New York, as had been the Twin Towers.

The killing by American troops of al-Qaeda founder Osama bin Laden in May last year has also helped draw a line under 9/11, as has the opening of the ground zero memorial, where last year’s ceremonies were held.

The memorial’s long delayed museum now appears set to be opened after Mayor Michael Bloomberg and New York Governor Andrew Cuomo reached an accord late on Monday over funding.

Last week, Obama said in a radio address that the United States is “stronger, safer and more respected in the world” since 9/11.

Underlining US successes in targeting al-Qaeda leaders, bin Laden’s successor Ayman al-Zawahiri released a video on the eve of this year’s anniversary in which he confirmed that his deputy, Abu Yayha al-Libi, had been killed in a drone strike in Pakistan in June.

Libi was considered al-Qaeda’s global propaganda mastermind and his death dealt the biggest blow to the group since the killing of bin Laden.

However, the Taliban scorned the idea that they are defeated, saying in Afghanistan that the United States faces “utter defeat in Afghanistan militarily, politically, economically and in all other facets.”

Most foreign troops are scheduled to withdraw by the end of 2014, handing over responsibility for combat to Western-backed Afghan government forces.