WASHINGTON — Barack Hussein Obama launched his second term as the nation’s 44th president Monday, urging the nation to move past polarizing debates and live up to its founding ideals by uniting to solve the country’s problems.

“America’s possibilities are limitless, for we possess all the qualities that this world without boundaries demands: youth and drive, diversity and openness, an endless capacity for risk and a gift for reinvention,” he said on a crisp, sun-filled afternoon. “My fellow Americans, we are made for this moment, and we will seize it, so long as we seize it together.”

His 18-minute inaugural address offered a clear agenda for his second term, marshaling the federal government to protect the rights of gay and lesbian people, combat climate change, provide opportunities for illegal immigrants, and help the downtrodden and middle class get a better foothold in a changing and still fragile economy.

A sea of spectators packed the National Mall to watch Obama, 51, sworn into office a few minutes before noon on the west side of the U.S. Capitol. First lady Michelle Obama and daughters Malia, 14, and Sasha, 11, looked on, as did former Democratic Presidents Jimmy Carter and Bill Clinton. The two living Republican former presidents, the ailing George H.W. Bush and son George W. Bush, didn’t attend.

“O-bam-a!” the crowd chanted. “O-bam-a!”

With grayer hair than when he took office four years ago, Obama had started his second term 24 hours earlier, after a brief private ceremony at the White House. Monday’s proceedings followed the tradition of delaying the public inauguration a day when the date prescribed by the Constitution falls on a Sunday.

The nation’s 57th inauguration consisted of five days of patriotic parades and fancy balls, solemn prayers and countless receptions for donors and supporters.

Monday’s events were jubilant, but they didn’t have the same level of excitement as four years ago, when a young senator promising hope and change became the nation’s first black president. Officials estimated that as many as 1 million people turned out for the festivities, compared with almost 2 million in 2009.

The crowds led to a maze of street closures, clogged subways, heightened security and the National Mall filled with 1,500 portable toilets, five large-screen TVs and 6,000 members of the National Guard assisting with crowd control.

Obama used his inaugural address to encourage those with differing views to work together to accomplish something, even if it’s not everything.

“For now decisions are upon us, and we cannot afford delay,” he said. “We cannot mistake absolutism for principle, or substitute spectacle for politics, or treat name-calling as reasoned debate,” the president said. “We must act; we must act knowing that our work will be imperfect.”

Obama, in a polarized political climate, must address fiscal issues — tax revisions and spending cuts — and pressing international obligations: stopping Iran’s nuclear program, ending war in Afghanistan and avoiding tensions with China over the administration’s “pivot” to Asia. In the weeks since he defeated Republican Mitt Romney, he has battled with Republicans in Congress over tax increases and spending reductions.

Outlining the nation he envisions, he sounded the themes of his recent campaign as a call for using the federal government to shift the benefits of the country and its economy to the poor and middle class and away from the wealthy.

“We, the people, understand that our country cannot succeed when a shrinking few do very well and a growing many barely make it,” he said. “We believe that America’s prosperity must rest upon the broad shoulders of a rising middle class.”

He linked past sacrifices to current struggles for equality for all: economic equality for the poor, civil rights for gays, equal pay for women.

“We, the people, declare today that the most evident of truths — that all of us are created equal — is the star that guides us still,” Obama said. “Just as it guided all those men and women, sung and unsung, who left footprints along this great Mall, to hear a preacher say that we cannot walk alone; to hear a King proclaim that our individual freedom is inextricably bound to the freedom of every soul on Earth.”

Republicans, who joined Obama at the White House in the morning for coffee and later at the Capitol for lunch, expressed hopes that the two sides could work together on fiscal issues.

“The president’s second term represents a fresh start when it comes to dealing with the great challenges of our day; particularly, the transcendent challenge of unsustainable federal spending and debt,” Senate Minority Leader Mitch McConnell, R-Ky., said. “Republicans are eager to work with the president on achieving this common goal, and we firmly believe that divided government provides the perfect opportunity to do so. Together, there is much we can achieve.”

The Obamas and Bidens started their day with a prayer service at St. John’s Episcopal Church a few blocks from the White House. A few hours later, Chief Justice John Roberts Jr. administered the 35-word oath.

On a day the nation honors Martin Luther King Jr., Obama placed his hand on two Bibles — King’s traveling Bible and the burgundy velvet-covered Lincoln Bible. Obama also had used the Lincoln Bible four years ago, the first to do so since it was used by Abraham Lincoln himself.

Michelle Obama smiled broadly, while even members of Congress snapped photos with their phones.

“Congratulations, Mr. President,” Roberts said just before a 21-gun salute boomed.

Minutes before Obama’s oath, Vice President Joe Biden was sworn in by Associate Justice Sonia Sotomayor, the first Hispanic and fourth female judge to administer the oath.

Afterward, Obama and Biden headed to the Capitol’s Statuary Hall to dine on steamed lobster and hickory grilled bison at a luncheon attended by 200, including Supreme Court justices and congressional leaders, sitting at tables adorned with bright orange flowers. Obama was presented with a custom hand-cut crystal Lenox vase with an etching of the White House. The tradition of the luncheon dates to President William McKinley in 1897.

House Speaker John Boehner, R-Ohio, presented Obama and Biden with the flags that flew over the Capitol. “To you gentlemen, I say congratulations and Godspeed,” he said.

Later, the Obamas led an inaugural parade — featuring eight official floats, 59 groups, 9,000 people, 1,500 service members and 200 animals — the 1.7 miles from the Capitol up Pennsylvania Avenue to the White House. They sat in a reviewing stand adorned with bulletproof glass and the presidential seal in front of the White House. Most of the onlookers waved American flags, but a handful of protesters held “God hates Obama” signs.

In the evening, the president and first lady were to attend two official inaugural balls, one for members of the military and another for the public. About 40,000 ticketholders were expected to fill the Washington Convention Center to hear Alicia Keys, Usher and Soundgarden and, hopefully, to catch a glimpse of the first couple.

“Last time there was a little bit more excitement. It was brand new,” Kerry Kelty of Pittsburgh said of Obama’s first inauguration. “I don’t think people are disappointed, but reality hit.”