With hundreds of thousands looking on from a packed Mall, President Obama took the oath of office for a historic second term on Monday morning, using his inaugural address to cast modern-day priorities — fighting climate change, welcoming immigrants and ensuring gay rights — as the extension of a long struggle to live up to the Founders’ ideals.

“Being true to our founding documents does not require us to agree on every contour of life. It does not mean we all define liberty in exactly the same way or follow the same precise path to happiness,” Obama said, speaking to a flag-waving crowd that jammed the Mall all the way to the Washington Monument.

“But,” he continued, “it does require us to act in our time.”

“My fellow Americans,” he added, “we are made for this moment and we will seize it, so long as we seize it together.”

Obama, 51, took the oath at 11:50 a.m., on a gray and chilly day in Washington. In 2009, he was the first African American to be sworn in as president; on Monday he became the first to do it twice.

A few hours later, Obama and First Lady Michelle thrilled the gathered crowds with a hand-in-hand stroll down Pennsylvania Avenue at the head of the inaugural parade. Onlookers waved and chanted “Obama!” and “Four more years!” along the street, while others cheered from several rooftops along Pennsylvania. Scores of bands, infantry regiments and custom-made floats followed. The parade ended shortly after 6:30 p.m., about the same time guests started showing up at the Washington Convention Center for the official Inaugural Ball.

The public inauguration had less of the stoic reserve that marked Obama’s first inauguration four years ago, held as the country sank deeper into recession. This ceremony featured two performances by pop stars: Kelly Clarkson sang “My Country, ’Tis of Thee,” and Beyonce sang the National Anthem. Though the crowd was smaller than four years ago, Obama’s inaugural call to broaden equality in the country carried a special significance for many in the crowd since it came on the day set aside to honor Dr. Martin Luther King Jr.

Obama’s address also seemed more optimistic than his 2009 speech, in which he warned a recession-wracked country about a trying winter ahead. It also revealed a president who doesn’t have to face another election: Obama’s words on gay rights, and on climate change, reflected a more aggressive tone than he showed in parts of his first term.

But the ceremony was also weighted with references to American history — both its triumphs and its bloody tragedies. The ceremony was held on Martin Luther King Jr. Day. A choir sang “The Battle Hymn of the Republic,” an anthem of the Union cause in the Civil War. And Obama swore his oath on a battered Bible used by Abraham Lincoln.

The invocation was given by another icon of the Civil Rights era: Myrlie Evers-Williams, whose husband Medgar Evers was slain in Mississippi in 1963.

Evers-Williams spoke of “witnesses — unseen by the naked eye, but all around us — thankful that their living was not in vain.”

After taking his oath, Obama gave a 19-minute address that, at times, had the itemized, agenda-setting feel of a State of the Union speech. It did not soar; it hurried — reflecting a president with a long agenda, and a short window left to make it happen.

Obama mentioned tax reform, Medicare, Social Security and Newtown, Conn., where December’s shooting rampage spurred Obama’s new push for stronger gun laws.

He also made a forceful pitch for action on climate change, a priority stymied by congressional opposition during Obama’s first term.

“We will respond to the threat of climate change, knowing that the failure to do so would betray our children and future generations,” Obama said. “Some may still deny the overwhelming judgment of science, but none can avoid the devastating impact of raging fires and crippling drought and more powerful storms.”

Obama also made a historic mention of gay rights: he apparently is the first president to ever utter the word “gay” in an inaugural address. In Obama’s list of key civil-rights turning points, there was “Selma,” for the march in Alabama in 1965. There was “Seneca Falls,” the town in New York where an 1848 convention helped launch the women’s rights movement. And then there was “Stonewall,” a reference to the 1969 Stonewall riots in New York City, considered the spark that created the modern gay-rights movement.

“Our journey is not complete until our gay brothers and sisters are treated like anyone else under the law,” Obama said. “For if we are truly created equal, then surely the love we commit to one another must be equal as well.”

In his address, Obama also invoked a theme from his reelection campaign: that of patience exhausted. The president said the politically gridlocked capital — and, implicitly, the Republicans who have fought his ideas — was moving too slowly at an urgent moment.

“We cannot mistake absolutism for principle, or substitute spectacle for politics, or treat name-calling as reasoned debate,” Obama said. “We must act, knowing that our work will be imperfect.”

The president’s audience appeared smaller than in 2009, when a record crowd of perhaps 1.8 million people watched Obama take his oath. As of 6 p.m., Metro said 657,000 riders had entered its rail system, compared with 923,000 at the same time four years ago.

Still, the Mall was crowded with thousands upon thousands, waving flags and chanting “O-BAM-A.” At 11:35 a.m., shortly after the ceremony began, U.S. Park Police said the area east of the Washington Monument was full and closed to additional visitors, who would have to gather farther to the west.

Police and National Guard officials said pedestrian traffic flowed throughout the morning without incident, although a few glitches at checkpoints and in some Metro stations were reported.

Metro station parking facilities filled up throughout the morning, and some stations near the Mall were overflowing, even though federal workers and many others had the day off for the Martin Luther King Jr. holiday.

At one spot on the Mall, in front of the Smithsonian castle, a predominantly African American crowd cheered, waved flags, took pictures and watched videos on the Jumbotron as accompanying music played at an ear-splitting volume. A National Park Service employee handed out Obama buttons. “You already paid for ’em,” he said.

On the grass, Sandra and Ronnie Robinson of Birmingham, Ala., set up folding chairs to watch the ceremony. Ronnie Robinson, 54, said he was in first grade when the 16th Street Baptist Church in Birmingham was bombed by white supremacists. Four little girls were killed.

Attending Obama’s inauguration on Martin Luther King Jr. Day, he said, “is the culmination to the dream. If we’re ever going to get close to the dream, this is as close as we’re going to get.”

Like the Robinsons, Katherine Ward, a Navy officer, was attending an inauguration for the first time. Ward, who is also African American, said she was serving in Iraq when Obama first took office.

“Now I’m here to cheer him on,” she said. “Everything Martin Luther King marched for and spoke on has come true.”

Up on the grand inaugural stage, Supreme Court Justice Sonia Sotomayor administered the oath of office to Biden at 11:47 a.m. Obama took the oath, administered by Chief Justice John G. Roberts Jr., at 11:50 a.m.

Earlier, Obama and his family had attended services at St. John’s Episcopal Church in Lafayette Square. Later, they drove in a long, slow motorcade down Pennsylvania Avenue, arriving at the Capitol.

“I miss this place,” Obama told reporters when he arrived. He served four years as a senator from Illinois before becoming president.

Members of Congress and other VIPs took their seats on the inaugural stage — senators stage left, and representatives, stage right — and did what mere mortals for blocks around were doing as well: taking photos of themselves. Sen. Patrick J. Leahy (D-Vt.), an avid photographer, snapped pictures of his colleague, Sen. Debbie Stabenow (D-Mich.) at the presidential lectern. House Majority Whip Kevin McCarthy (R-Calif.) captured a few images of the crowd and his colleagues.

In one row, from left to right, sat former president Bill Clinton, Secretary of State Hillary Rodham Clinton, former president Jimmy Carter and former first lady Rosalynn Carter.

On the Mall, there was Iris Murdock, 62, a retired school teacher from Baltimore, who began the journey to her first presidential inauguration well before dawn, driving to her daughter’s home in Hyattsville. There, the two women boarded a Green Line train.

They emerged at Federal Center before 7 a.m., when it was still dark. White lights twinkled on nearby trees as the gathering crowd bundled up against the cold.

“This was on my bucket list,” said Murdock, snug in a long coat and mittens. “You live in Baltimore, and it’s a hop, skip and a jump away.”

Murdock supports Obama, but she sees the inauguration as bigger than that. “It doesn’t matter what political party you are, it’s part of being an American,” she said. “You stand in line to vote. You have to see what the rest of it is like, too.”

As she talked, a group of middle-schoolers trooped past her, carrying souvenir-size flags and composition books. A smile spread across her face.

“I’m a retired educator,” she said, beaming. “Look at them.”

As the parade was winding down and crowds began to leave, Symone Brown and Brittany Gamble, both 18 and both from Baltimore, swept trash from Pershing Park. They were dressed in orange vests.

Brown and Brittany, who had signed up to work for a temp agency, arrived at 6 a.m.

Earlier in the day they helped people find their seat. Now they were filling blue bags with bottles, cigarette butts , discarded hand warmers

The money -- $8 an hour -- was nice, but this was more than a job.

“I feel like I’m part of history,” Gamble said, “me being 18 years old, just the thought of seeing Obama’s face.”

They both caught a glimpse through his limo window. They both voted for him in November, their first election.

Gamble said that getting up early Monday morning to take the bus down from Baltimore was tough. “The money was a motivator, but to be honest it was more to be there with Obama.”