However, he criticised CNN for failing to check their reports.
Remembrance services were held across the US for the victims of the 11 September 2001 attacks.
Adam Brookes, BBC News, Washington DC
The security establishment in Washington DC went into sudden overdrive on Friday morning after a major national news network began reporting a serious security incident on the Potomac river.
After a protracted period of confusion, US government agencies, including the Department of Homeland Security, the Pentagon and the FBI began saying that they had no reports of any shots fired.
Then, the US Coast Guard said that it had been conducting a training exercise on the Potomac. No shots had been fired, but a simulation might have involved the words "shots fired" being put over a radio network.
In the hair-trigger atmosphere of Washington DC on the anniversary of the 9/11 attacks, it is perhaps not a surprise that any security incident garners immediate attention, but there will no doubt be uncomfortable questions as to why the Coast Guard chose that particular moment to conduct an exercise.
Nearly 3,000 people died when the four planes crashed in New York, at the Pentagon and in a Pennsylvania field.
Speaking at the Pentagon on his first 9/11 anniversary as US president, Barack Obama said the years would not diminish the loss of that day.
"In the defence of our nation we will never waver," he said. "In pursuit of al-Qaeda we will never falter".
Accompanied by Defence Secretary Robert Gates, he met members of victims' families and laid a wreath.
Meanwhile, thousands gathered for ceremonies in a square near New York's Ground Zero.
Vice-President Joe Biden attended the New York ceremony, where planes crashed into the World Trade Center towers, causing them to collapse.
Volunteers who helped in the aftermath of the attacks joined family members in reading the more than 2,700 names of the victims.
Memorial held at Ground Zero
The BBC's Matthew Price in New York says the Ground Zero area remains a building site, despite plans for a memorial, a museum and five new skyscrapers.
Delays caused by political arguments and financial and legal disputes have left huge question marks over the entire project, he says.
At another ceremony at the site of the crash of United Airlines Flight 93 near Shanksville, Pennsylvania, former Secretary of State Colin Powell praised passengers on the flight who prevented the hijackers from flying the plane into their intended target.
Americans have also been encouraged to contribute to a national day of community service.
Conservation projects, aid packages for serving soldiers and the simple offering of work for free are among the undertakings made by members of the public.
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