Moments of silence were held for the almost 3,000 people killed when hijackers crashed planes into the World Trade Centre, the Pentagon and a field in Pennsylvania.
Bells first tolled at 8:46am – the time the first aircraft was smashed into the north tower by al Qaeda extremists.
They also rang out to mark other significant timings during that destructive day in 2001, including the moment the south tower collapsed in New York.
On the White House lawn, Mr Trump took part in a ceremony to remember the victims and then went to the Pentagon for a second commemoration.
Speaking in Virginia, the President issued a warning to extremists, saying “America cannot be intimidated” and those who try will join the list of enemies “who dared to test our mettle”.
He said when America is united then “no force on Earth can break us apart”.
Meanwhile, at Ground Zero in New York, victims’ relatives marked the anniversary by reading out the names of those who died.
Some said they could not believe that 16 years had passed since the tragedy.
For others, it was an occasion to urge for a return to the sense of unity they felt after the atrocities.
Magaly Lemagne, who lost her policeman brother David Prudencio Lemagne, said: “Our country came together that day. And it did not matter what colour you were, or where you were from.”
She implored people to “stop for a moment and remember all the people who gave their lives that day”.
“Maybe then we can put away our disagreements and become one country again.”
In Shanksville, Pennsylvania, Vice-President Mike Pence addressed hundreds of people, including relatives of victims of United Flight 93, at a sombre service.