Obama will be sworn in as the first African-American president at a time when US soldiers are fighting in Afghanistan and Iraq and the country is facing the worst economic crisis since the Depression in the 1930s.
Both issues were raised in his speech.
"In the course of our history, only a handful of generations have been asked to confront challenges as serious as the ones we face right now. Our nation is at war. Our economy is in crisis," Obama said.
"I won't pretend that meeting any one of these challenges will be easy. It will take more than a month or a year, and it will likely take many.
"But never forget that the true character of our nation is revealed not during times of comfort and ease, but by the right we do when the moment is hard.
"I ask you to help me reveal that character once more, and together, we can carry forward as one nation, and one people, the legacy of our forefathers that we celebrate today."
Security was tight, as helicopters circled over the city and armed police officers with sniffer dogs patrolled the area.
Early on Sunday morning, Obama and Joe Biden, the vice president-elect, laid a wreath at the Arlington National Cemetery's Tomb of the Unknowns, a war grave that symbolises the resting site of unidentified American soldiers.
As Obama drove to the cemetery in the state of Virginia and then through Washington's commercial district to attend a Baptist church service, groups of people gathered along the streets to wave and cheer as his motorcade passed.
Obama travelled from Philadelphia to Washington by train. The trip was designed to recall the 1861 rail journey to the capital by Abraham Lincoln before he entered the White House. Obama frequently evokes Lincoln, a fellow resident of Illinois, who led the US during the Civil War and ended slavery in America.
As the presidential inauguration approached, data showed that the US unemployment rate rose to 7.2 per cent in December.
Up to 2.6 million people have lost their jobs in the last year, the largest employment slump since 1945.
"These problems weren't made in a week or a year and they're not going to be fixed in a week or a month or a year," Lawrence Summers, the incoming director of the White House National Economic Council, said.
"There is no question, almost no question, that the economy is going to decline for some time to come."
Obama has vowed to spend hundreds of billions of dollars to jolt the country out of a deepening recession.