Mr Obama said that meeting the nation's challenges would not be easy
US President-elect Barack Obama has told a huge crowd of supporters at a pre-inauguration rally in Washington that "anything is possible in America".
As the US fights two wars and tackles an economic crisis, Mr Obama said he was "hopeful" the US would overcome its toughest challenges in generations.
He was speaking at a welcome concert on the steps of the Lincoln Memorial, ahead of his inauguration on Tuesday.
Some of the biggest names in music took part, among them Beyonce and U2.
Mr Obama said that solving the nation's problems would take time, and that the road would be long and the climb steep.
But he said that "despite the enormity of the task that lies ahead - I stand here today as hopeful as ever that the United States of America will endure - that the dream of our founders will live on in our time".
He said that men and women from different backgrounds asked "only for what was promised us as Americans - that we might make of our lives what we will and see our children climb higher than we did".
Mr Obama's remarks concluded the We Are One concert - one in a series of special events leading up to his swearing-in as the 44th US president on Tuesday.
Earlier Mr Obama placed a wreath at the Tomb of the Unknowns at the Arlington National Cemetery in Virginia to remember fallen American servicemen.
The BBC's Richard Lister in Washington says it was a reminder to his supporters that while there is room for celebration over the next few days, this is also a sombre time for America.
An unprecedented security operation is under way in the capital ahead of Mr Obama's swearing-in on Tuesday, with the authorities expecting a turnout of up to two million.
Some 240,000 tickets have been issued for the festivities at the Capitol.
For those without tickets, the entire length of the National Mall, which stretches nearly two miles from the Capitol to the Lincoln Memorial, will be open to the public for the first time.
A national holiday honouring the assassinated civil rights leader, Martin Luther King Day, falls on Monday - the eve of the inauguration of the first black US president.
Mr Obama, Vice-President-elect Joe Biden and their families will take part in activities in Washington aimed at encouraging others to help their communities.
On Saturday, Mr Obama retraced the steps of former US President Abraham Lincoln, travelling by train from Philadelphia to Washington.
The 137-mile (220 km) journey began at Philadelphia's 30th Street station, where Mr Obama said he would be carrying the hopes of ordinary Americans with him to Washington.
You can watch Tuesday's inauguration live on the BBC News website, as well as on BBC World News and BBC One.
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