But he said, "they will be met."
Describing the challenges ahead, he said: "That we are in the midst of crisis is now well understood. Our nation is at war, against a far-reaching network of violence and hatred.
"Our economy is badly weakened, a consequence of greed and irresponsibility on the part of some, but also our collective failure to make hard choices and prepare the nation for a new age.
"Homes have been lost; jobs shed; businesses shuttered. Our health care is too costly; our schools fail too many; and each day brings further evidence that the ways we use energy strengthen our adversaries and threaten our planet."
He said: "Every so often the oath (of office) is taken amidst gathering clouds and raging storms".
He said: "Power alone cannot protect us." The US would "begin to responsibly leave Iraq to its people and forge a hard-earned peace in Afghanistan".
He told the world's Muslims that his administration will be looking for a "new way forward, based on mutual interest and mutual respect."
And he is warning leaders around the globe who try to encourage conflict and "blame their society's ills on the West" that their people will judge them on what they build, not what they destroy.
He is also pledging to "work alongside" the people of poor nations to make "farms flourish and let clean waters flow."
Barack Obama was speaking after he made history when he was sworn in as the first black US president, riding a wave of public optimism he will need to tap to deal with the worst economic crisis in 70 years and two wars.
An estimated million people, bundled up against the cold and in a festive mood, packed Washington's Mall, which stretches 2 miles from the Capitol to the Lincoln Memorial on the Potomac River, and along Pennsylvania Avenue to the White House.
Obama, a Democrat, was due to be sworn in as the 44th US president just before noon EST (1700 GMT), taking over from Republican George Bush.
The inauguration was taking place amid unprecedented security. About 8,000 police were deployed and a total of 32,000 military personnel were on duty or on standby.
The Homeland Security Department said authorities were investigating a potential threat of "uncertain credibility" in connection with the inauguration.
This will be the first inauguration of a new president since the Sept. 11, 2001, attacks that took place early in Bush's two-term presidency and shaped his policies, prompting Washington's war on terrorism. Obama's election has also stirred white supremacists to anger, sparked arrests during his campaign and raised assassination fears.
Major US stock indexes fell on Tuesday on mounting worries over grim earnings and the health of the banking sector, highlighting the scale of the financial problems Obama will face.
The inauguration of Obama, 47, the son of a black Kenyan father and a white mother from Kansas, will be full of ceremony, and full of symbolic meaning for African-Americans, who for generations suffered slavery and then racial segregation that made them second-class citizens.
Obama was set to take the oath of office with his hand on a Bible used by Abraham Lincoln at his first inauguration in 1861, standing on the western steps of the capitol, a building that was partly built by black slaves.
Some estimates put the number of people expected to pack the Mall and inaugural parade route at more than 2 million. Crowds clogged the city's metro rail system and thronged the security check-points.
A 68-year-old woman was hit by a train at the crowded Gallery Place downtown metro station after she fell to the tracks. She was alive when emergency personnel removed her, authorities said. The incident caused delays on the rail line serving the station near the heart of the action.
"This is chaos now," said Judy Bailey, 42, of Cincinnati, Ohio, as police shunted her further and further away from the swearing-in ceremony early in the morning. "But it is amazing to be here. This is history in the making."
Polls show widespread support for Obama and optimism about the coming four years of his presidency, despite a deepening recession that has saddled the country with a $1 trillion deficit and 11 million people unemployed.
Bush is leaving office having plumbed record lows in approval ratings.
Obama, a former Illinois senator who capped a hard-fought election campaign with a comfortable win against Republican John McCain in November, has stressed that the time to party and celebrate will be short-lived.
On Wednesday he will start shepherding an $825 billion economic stimulus plan through Congress.
He faces daunting challenges - economic turmoil, the wars in Iraq and Afghanistan, global warming, conflict in Gaza, tensions between Pakistan and India and a resurgent Russia.
But analysts say that at least for now, it will be his ability to revive the recession-hit economy that will be the benchmark by which his presidency is judged.
The Washington Post reported that in one of his first actions as president, Obama planned to name former Sen. George Mitchell as his Middle East envoy in one of his first actions as the new US president.
Obama is expected to meet military commanders on Wednesday to discuss the US troop withdrawal from Iraq, to fulfill a campaign pledge to withdraw all troops within 16 months.
Obama's swearing-in will be followed by the US Marine Corps band playing "Hail to the Chief" and a 21-gun salute.
Obama will then to deliver his eagerly anticipated inauguration speech, expected to last about 20 minutes, just after midday.
"He is going to lay out a lot of the challenges we face as a country, but he will also remind ... that America has faced great challenges before," his spokesman Robert Gibbs told CNN on Tuesday.
"He will talk about responsibility, particularly the great responsibility in the action of government and financial institutions, some of whose actions have got us into the mess we are in now."
He played down suggestions that Obama could issue executive orders as early as Tuesday to close the US military prison at for foreign terrorism suspects at Guantanamo Bay and repeal a ban on overseas funding for clinics or groups which provide abortion services.
The Guantanamo prison has been a lightning rod for broad world disapproval of many Bush policies in the US war on terrorism.
Gibbs said some announcements would be made later in the week.
Obama and his wife, Michelle had coffee at the White House with the Bushes and Vice-President Dick Cheney and his wife after attending a church service. Obama then headed toward the Capitol for the swearing-in ceremony.
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