9/11 anniversary: Obama calls for a future with hope
US President Barack Obama has told Americans they should honour those who died in the 9/11 attacks, but look to the future with "hearts full of hope".
He said the decade since the attacks showed Americans' resolve to defend their way of life.
The ideal that "men and women should govern themselves... has only been strengthened", he said.
Nearly 3,000 people died when four hijacked airliners crashed in New York, Washington and Pennsylvania.
Mr Obama was speaking during a memorial concert at the Kennedy Center in Washington, closing a day of official commemorations of the 10th anniversary of the attacks,
Earlier in the day he had attended memorial ceremonies at the three sites where four airliners hijacked by al-Qaeda militants crashed: the World Trade Center in New York, the Pentagon in Washington and a Pennsylvania field.
A minute's silence marked each moment that a plane struck, or one of the WTC's twin towers fell.
Security was tight following warnings of a possible new attack by al-Qaeda.
President Obama said that much had changed for Americans since 11 September 2001.
"We've known war and recession; passionate debates and political divides. We can never get back the lives that were lost on that day, or the Americans who made the ultimate sacrifice in the wars that followed.
"Yet today, it is worth remembering what has not changed," he said.
"Our character as a nation has not changed... Our belief in America, born of a timeless ideal that men and women should govern themselves; that all people are created equal, and deserve the same freedom to determine their own destiny - that belief, through test and trials, has only been strengthened."
Mr Obama paid tribute to the victims of the attacks as well the courage of the survivors.
He also lauded the "two million Americans who have gone to war since 9/11. They have demonstrated that those who do us harm cannot hide from the reach of justice, anywhere in the world."
In the months that followed 9/11, US forces were sent to Afghanistan to oust the Taliban from power for giving sanctuary to al-Qaeda.
In 2003, the US led an invasion of Iraq that overthrew Saddam Hussein.
More than 6,200 members of the US military have been killed in the wars in Iraq and Afghanistan.
Earlier in the day, a memorial to the 9/11 victims was unveiled at the site of the World Trade Center.
All of the victims' names were read out amid tears, the five-hour reading punctuated by the solemn silences, and music.
Bagpipers opened the gathering, the Brooklyn Youth Chorus sang the national anthem, the cellist Yo-Yo Ma performed, and Paul Simon played his classic song The Sound Of Silence.
Mourners streamed into the newly opened memorial, which has two reflecting pools, each almost an acre in size, in the footprints of the twin towers.
They placed pictures and flowers beside names etched in bronze. Grown men and women sobbed in grief over the inscriptions.
Behind the memorial could be seen the gleaming bulk of One World Trade Center, now three-quarters completed.