"As Americans, we draw strength from you, for your love is the ultimate rebuke to the hatred of those who attacked us that bright, blue morning," Obama said to relatives of victims at the Pentagon.
Ceremonies of remembrance were held in New York and Washington, against the backdrop of Obama's pledge to "destroy" Islamic State fighters in Iraq and Syria -- a new front in the war on radical Islam begun in earnest 13 years ago.
"You've kept alive a love that no act of terror can ever extinguish," he said.
"We carry on because as Americans, we do not give in to fear. Ever."
Obama, and First Lady Michelle Obama and Vice President Joe Biden observed a moment of silence on the White House south lawn, along with about 300 staffers. Flags in Washington flew at half-mast.
With agency inputs