WASHINGTON — In a swift and simple ceremony at the White House, President Barack Obama was sworn in for a second term Sunday and embarked on another four years leading a nation hobbled by a weak economy and gripped by political division.

With his family at his side and his hand on his wife’s family Bible, the 44th president began the new term on an understated note, repeating the oath of office in a private ceremony the day before a more lavish, public re-enactment.

The intimate event was an adherence to tradition prompted by a quirk of the calendar. Under the Constitution, a president’s term ends at noon Jan. 20. When that date falls on a Sunday, presidents have shifted the public ceremony a day and opted for a swearing-in at the White House.

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Obama stood in the Blue Room, an elegant oval parlor, next to first lady Michelle Obama and their daughters, Malia and Sasha. Chief Justice John G. Roberts Jr. administered the 35-word oath more smoothly than he did four years ago when he flubbed the phrasing. Other relatives watched but remained out of view of the television cameras. The entire event took about a minute.

“I did it,” the president said as he hugged his family afterward.

“Good job, Dad,” 12-year-old Sasha said. “You didn’t mess up.”

The event bore little resemblance to the full display of traditional pageantry planned for today. Although a pared-down version of Obama’s first inauguration four years ago, the public swearing-in still is expected to draw about 800,000 to the National Mall to watch the poetry, music and oratory outside the U.S. Capitol.

The ceremony will take place on Martin Luther King Day and will include several nods to this president’s place in history as the first African-American to hold the office. Obama plans to place his hand on two Bibles, one owned by the slain civil rights leader and another used by Abraham Lincoln at his swearing-in on March 4, 1861.

In his address, the president will call for a shared search for areas of compromise. “He is going to talk about the fact that our political system doesn’t require us to resolve all of our disputes or settle all of our differences,” senior Obama political adviser David Plouffe said Sunday on CNN’s “State of the Union.” “But it does impel us to act where there should be, and is, common ground.”

The final hours of Obama’s first term were filled with quiet moments and personal reflection.

The president began his day at Arlington National Cemetery, where he and Vice President Joe Biden, fresh from his own swearing-in, laid a wreath at the Tomb of the Unknowns under a clear-blue winter sky.

From there, the president and first lady, infrequent churchgoers, made a visit to a historically black church, Metropolitan African Methodist Episcopal, the oldest A.M.E. church in the nation’s capital. Obama, who almost never discusses his own place in history, sat in the pews where 119 years ago congregants listened to one of Frederick Douglass’ last calls for racial equality.

“Put away your race prejudice. Banish the idea that one class must rule over another,” the abolitionist and former slave said in the 1894 speech, “The Lessons of the Hour.”

Obama listened to a reading from Exodus — the final passages detailing the flight of Moses and the Israelites out of slavery in Egypt. In his sermon, the Rev. Ronald E. Braxton urged the president to overcome obstacles and continue “forward,” echoing Obama’s re-election slogan.

Obama’s legislative agenda faces plenty of obstacles, most notably a Republican-led House of Representatives that for two years has tried to block his attempts to raise taxes on the wealthy and to use government spending to create jobs. Obama’s second-term priorities — an overhaul of the immigration system and new gun-control measures — are facing solid opposition.

Biden took his oath of office in an event that appeared lively compared to the president’s austere one — a contrast that may reflect their personalities and political futures.

The vice president, who may be a candidate for the top job in 2016, gathered about 120 friends, family members and Democratic power players to his official residence at the Naval Observatory. The event included political strategists, labor leaders and party officials. Many came early for a Catholic Mass and stayed afterward for breakfast.

“It’s an honor. It’s an honor,” Biden told Supreme Court Justice Sonia Sotomayor immediately after she administered the oath, the fourth female jurist — and first Latina — to perform that duty for a president or vice president.

His remarks were unusually brief for a politician known for his loquacious and sometimes gaffe-ridden speeches. The night before, Biden had told supporters at the Iowa inaugural ball he was “proud to be president of the United States.” He quickly corrected himself, saying he was “proud to be Barack Obama’s vice president.”

At the White House, Obama’s swearing-in was apolitical, personal and cautious.

On his guest list were just a dozen relatives, including his half sister, Maya Soetoro-Ng, and brother in-law, Craig Robinson.

Roberts and Obama proceeded carefully through the oath, the third time the duo have gone through it. At Obama’s first inaugural in 2009, they mangled the wording, prompting White House lawyers, out of an abundance of caution, to summon the chief justice to the White House for a do-over.

This time, with Roberts reading the oath from a piece of paper, it went off without a hitch.

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