Barack Obama, joined by his wife, Michelle, and daughters, Sasha and Malia, takes the oath of office from Chief Justice John Roberts to become the 44th president of the United States at the U.S. Capitol. (Jae C. Hong/Associated Press)

Americans need to embrace a "new era of responsibility" to remake the United States in the face of military, economic and domestic challenges, U.S. President Barack Obama said Tuesday in his inauguration address.

"Starting today, we must pick ourselves up, dust ourselves off, and begin again the work of remaking America," said Obama, who spoke before more than one million people crowded into Washington's National Mall, a park that stretches from the Lincoln Memorial to the Capitol.

Obama made the historic address shortly after he held his right hand in the air and placed his left hand on Abraham Lincoln's inaugural Bible to take the oath of office and become the first black president of the United States.

"What is required of us now is a new era of responsibility — a recognition, on the part of every American, that we have duties to ourselves, our nation, and the world," he said.

"Duties that we do not grudgingly accept but rather seize gladly, firm in the knowledge that there is nothing so satisfying to the spirit, so defining of our character, than giving our all to a difficult task. This is the price and the promise of citizenship."

On the morning of the inauguration, outgoing President George W. Bush and his wife, Laura Bush, welcomed president-elect Barack Obama and his wife, Michelle Obama, on the north portico of the White House. (Pablo Martinez Monsivais/Associated Press)

Obama, a Democrat who succeeds Republican George W. Bush as president, acknowledged his oath was administered "amidst gathering clouds and raging storms" — an economy in crisis, costly health care, a faltering school system and environmental threats.

"That we are in the midst of crisis is now well understood," said Obama. "The challenges we face are real.

"But know this America — they will be met," he said, drawing a massive cheer from the crowd.

Obama vowed to rebuild infrastructure, invest in scientific research, improve health care and find new sources of energy.

"Those who manage the public's dollars will be held to account," he said.

Obama also issued a blunt warning to those who threaten the United States: "We will not apologize for our way of life, nor will we waver in its defence, and for those who seek to advance their aims by inducing terror and slaughtering innocents, we say to you now that our spirit is stronger and cannot be broken; you cannot outlast us, and we will defeat you."

Lincoln's Bible used for oath

The 47-year-old former Illinois senator was sworn in by Supreme Court Chief Justice John Roberts. Michelle Obama, wife of the president, carefully held Lincoln’s Bible, which hasn’t been used since Lincoln took the oath of office in 1861.

But Obama stopped abruptly when Roberts reversed some of the words of the 35-word oath that is prescribed by the Constitution. The oath includes the phrase "that I will faithfully execute the office of president of the United States," but Roberts misplaced the word "faithfully," saying it only after he said "president of the United States."

Crowds gathered early on Washington, D.C.'s National Mall for the swearing-in ceremony. (Ron Edmonds/Associated Press)

Obama appeared to realize something wasn't right and stopped at the word "execute."

Roberts then repeated the phrase, putting "faithfully" in the right place but without repeating "execute." Obama then repeated Roberts's original, incorrect version putting the word "faithfully" after president of the United States. They continued on from there.

Earlier, Obama had arrived at the U.S. Capitol, travelling together with the outgoing president in a motorcade from the White House, where Bush had hosted the Obamas, and incoming vice-president Joe Biden and his family, for coffee.

Bundled against the cold but determined to witness history, hundreds of thousands of people streamed into the National Mall to witness Obama become the 44th president at noon.

"I've been real emotional all morning thinking about my grandmother and the heroes whose shoulders we stand on. They'd be so proud," said spectator Lyshundria Houston, who travelled 20 hours from Memphis, Tenn., to watch the inauguration ceremony in Washington.

'We will not apologize for our way of life, nor will we waver in its defence...'—Barack Obama

The new president wore a red tie and white shirt with his new tuxedo made by Hart Schaffner Marx, a unionized factory in Chicago. This was topped with an overcoat adorned with an American flag pin.

Michelle Obama wore a sparkling yellow-gold sheath dress with matching coat by Cuban-born American designer Isabel Toledo. She paired the ensemble with green gloves from J. Crew and green shoes.

Bush leaves note for Obama

Security in Washington was unprecedented, with law enforcement officials scanning and scouring the area, including sharpshooters, air patrols, bomb-sniffing dogs, U.S. coast guard patrol boats along the Potomac River and more than 5,000 security cameras.

Defence Secretary Robert Gates was chosen to be the "designated successor" in case of an attack at the ceremony. In the past, presidents have designated one cabinet member or other official to take the reins of government if there is a calamity at the inauguration. Gates was kept at an undisclosed location during the event.

Obama and his wife left Blair House shortly before 9 a.m. for a private prayer service at St. John's Episcopal Church before travelling to the White House to have coffee with the outgoing Bush. The two men, along with their families, rode together in a heavily armoured Cadillac limousine nicknamed "the beast" to the Capitol.

Officials said Bush, following in the tradition of past presidents, left a personal letter in the top desk drawer for the incoming commander-in-chief. The contents of the letter were not made public, but White House press secretary Dana Perino said Bush wished Obama well and called his term a "fabulous new chapter" in American history.

Following the swearing-in ceremony, the Bush family travelled to Andrews Air Force Base to board a plane that was to fly them to Midland, Texas. Later, they were to travel to the family ranch in Crawford.

Late in the afternoon, Obama and his wife got out of the limousine leading the inaugural parade along Pennsylvania Avenue and walked for a few blocks. Thousands of spectators lining the parade route loudly cheered as the couple, waving to the crowd, made their way down the street before returning to the car.

They were followed by more than 10,000 people representing various school bands and military honour guards who travelled from Capitol Hill to the White House.

Toronto's Nathaniel Dett Chorale, a group dedicated to Afrocentric music, was to perform as the inauguration parade passed in front of the Canadian Embassy on Pennsylvania Avenue. The chorale is Canada's gift to Obama.

"I think a lot of what Obama embodies, his message of inclusively and trying to work together as one and break down some of the walls, resonate with our mission. It's what we try to do through our music," said chorale founder and artistic director Brainerd Blyden-Taylor.

About 1,000 people were invited to a "tailgate" party on the embassy's raised courtyard, which offers one of the best views of the Capitol. Guests were to dine on Alberta grilled sausages, Canadian beer and BeaverTails, the deep-fried pastry popular among skaters on the Rideau Canal in Ottawa.

10 inaugural balls Tuesday night

Obama and his wife were to spend the evening attending 10 official inaugural balls, beginning with the Neighborhood Ball for those living in the Washington, D.C., area.

U.S. President Barack Obama, left, and his wife, Michelle Obama, dance together at the Neighborhood Inaugural Ball in Washington, D.C., Tuesday night. (Alex Brandon/Associated Press)

During their first dance, the president and Michelle performed an intimate slow dance to Etta James's At Last, sung by pop star Beyoncé. Obama wore a white tie to match his wife's one-shouldered, floor-length Jason Wu gown embellished with white floral details.

Obama said the ball best captured the spirit of his campaign.

"We got the idea for the neighbourhood ball because we are neighbourhood people," he said. "I cut my teeth doing neighbourhood work, and this campaign was organized neighbourhood by neighbourhood."

Celebrations for the next presidency began on the weekend, with Obama's whistle-stop tour from Philadelphia to Washington, along the path Lincoln took in 1861. That followed a celebrity-filled concert where several hundred thousand people flanked the reflecting pool on the National Mall in Washington, D.C., hearing actors, singers and then Obama himself rally for national renewal.

On Monday evening, Obama attended three private dinners to honour former secretary of state Colin Powell, Biden, a longtime senator from Delaware, and Senator John McCain, the 2008 Republican presidential nominee.

Michelle Obama hosted a children's evening concert.

On the eve of the inauguration, Prime Minister Stephen Harper wished the president-elect well, but added that "nobody is under any illusion" about the challenges he faces, including the economic meltdown.

"If I were in his position, on the economic side, there would be two [priorities] high on my list. One is the stimulus package and getting that right," he said.

Harper also urged Obama to continue trying to stabilize the financial sector in the United States.

"This will remain a major challenge to the world economy until it is fixed," he added.

With files from the Associated Press and the Canadian Press