The president said that maintaining a shared purpose to oppose "terrorism" would be the most effective way to stand against those who wish to strike the US.
"Let us renew our resolve against those who perpetrated this barbaric act and who plot against us still," he said.
"In defence of our nation, we will never waver."
Obama's derfiant words were accompanied by a brief moment of alarm in the capital as authorities raised an alarm after spotting a suspicious boat on the Potomac river near the Pentagon, but the vessel was later identified as a US Coast Guard boat on a training exercise.
"We will never forget the rage and aching sadness we felt"
Police and federal law officials denied media reports that shots had been fired during the incident.
"We are still gathering information of how this training event might have been misconstrued as an actual incident. We will conduct a thorough review of this incident," the Coast Guard said in a written statement.
Obama had earlier observed at the White House a moment of silence at 8:46am (1346GMT), the minute when the first of two hijacked passenger aircraft struck one of the two World Trade Centre towers on September 11, 2001.
About 500 people attended the Pentagon memorial service, including families of the victims and survivors of the Pentagon attack.
Joseph Biden, the vice-president, laid a wreath at Ground Zero in New York, where the twin towers of the World Trade Centre once stood.
In a message to the city that was published on the front page of a daily newspaper, Obama said Americans were in solidarity with New Yorkers on the anniversary of the attacks.
|Thousands of people died in the attacks on the
World Trade Centre towers in New York [AP]
Obama's letter in the New York Daily News
said that the attacks on the World Trade Centre "will be forever seared in the consciousness of our nation" and that "every year on this day, we are all New Yorkers."
"We will never forget the images of planes vanishing into buildings; of billowing smoke rolling down the streets of Manhattan; of photos hung by the families of the missing," he wrote.
"We will never forget the rage and aching sadness we felt. And we will never forget the feeling that we had lost something else: a sense of safety as we went about our daily lives."
The president said that the war in Afghanistan, which was undertaken weeks after the September 11 attacks and which has become increasingly unpopular among Americans, was an intrinsic part of his strategy "to take the fight to the extremists who attacked us on 9/11".
But he also said that the US should lead through "the power of our fundamental values", and not just rely on the use of military force.
The president is considering whether to send extra troops to Afghanistan in an effort to confront a resurgent Taliban, but opponents say clarity is needed on the Afghan mission first.
Carl Levin, a Democrat who chairs the senate's armed services committee, said on Thursday that the US government's goal should be to provide sufficient training to Afghan forces, so that they can take control of security, rather than sending thousands more US troops to Afghanistan.
Marwan Bishara, Al Jazeera's senior political analyst, said: "The Democratic leadership in congress are not really encouraged to send more troops to Afghanistan.
"Even right-wing media commentators are advocating redeployment of troops from the [centre of] Afghanistan to its periphery, so that the war can be run from there.
"There is less and less will among the US elite and the public to escalate the war, and people are getting more and more confused about the objectives.
"General Petraeus [the commander of US Central Command] tells us that there are no more al-Qaeda in Afghanistan; he says they are in Pakistan."