A self-assured President Obama on Monday used his second inaugural address to lay out a bold liberal vision of the American future, drawing direct links between the origins of the republic and some of the most vexing political issues of the day.

The usual inauguration choreography of prayers and poems and crowds became a powerful demonstration of history’s arc: The first African American president was taking his second oath of office on a day named for the Rev. Martin Luther King Jr. on the Mall where King thundered almost 50 years ago about the United States’ unfulfilled promise.

On a day when the president was at times confident and wistful, solemn and jubilant, he called on the American people to join him in creating a new nation grounded in the old ideas of equality and opportunity.

“What makes us exceptional, what makes us America, is our allegiance to an idea articulated in a declaration made more than two centuries ago,” Obama said. “We hold these truths to be self-evident, that all men are created equal.” He linked the struggle for civil rights and women’s suffrage to the debate over same-sex marriage, and promised to address immigration and climate change.

“We the people still believe that our obligations as Americans are not just to ourselves, but to all posterity,” he said.

Richmond, Va. native, Erica Edwards, shares her thoughts and opinions about President Obama’s Inauguration speach at the National Mall earlier today. (Annie Gowen/The Washington Post)

Obama spoke to a throng bundled against the cold in scarves and hats. Attendees had come by plane, by car and crowded Metro to see his second inauguration.

Myrlie Evers-Williams, widow of slain civil rights activist Medgar Evers, spoke of “a great cloud of witnesses — unseen by the naked eye, but all around us — thankful that their living was not in vain.”

The 181 / 2-minute address showed a president who was seeking to shake off the personal caution and political gridlock that had hemmed in his ambitions before. His speech did not soar as much as it hurried: bouncing from goal to goal, building an agenda that could define his party — and his legacy.

“We cannot mistake absolutism for principle, or substitute spectacle for politics, or treat name-calling as reasoned debate. We must act, knowing that our work will be imperfect,” Obama said, in an address that quoted the Declaration of Independence, and repeated the opening words of the Constitution’s preamble: “We the people.”

“We must act, knowing that today’s victories will be only partial,” Obama said. “And that it will be up to those who stand here in four years — and 40 years, and 400 years hence — to advance the timeless spirit once conferred to us in a spare Philadelphia hall.”

Obama was the first president to use the word “gay” in his inaugural address. He had made outreach to gay voters and gay donors a key part of his reelection strategy. On Monday, he cast the battle for gay rights as part of a longer, broader struggle to make good on the declaration’s promise that “all of us are created equal.”

Obama listed three turning points: There was Seneca Falls, the town in New York where a convention in 1848 helped launch the women’s rights movement. There was Selma, referring to a civil rights march in Alabama in 1965.

And then there was Stonewall, a reference to 1969 riots in New York City that were considered the spark that created the modern gay-rights movement. The Stonewall Inn was a bar made famous by a police raid. Obama seemed to be saying that this unlikely place belongs among the hallowed spots of American history.

“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.”

Sitting in a reviewing stand near the White House was Jody Huckaby, the executive director of the activist group Parents, Families and Friends of Lesbians and Gays. “It’s monumental. It’s historic,” he said afterward. The message, as he saw it: “The American promise . . . this administration is serious about it for everyone.”

As Obama spoke from the Capitol’s West Front, a flag-waving crowd spilled down the Mall toward the Washington Monument. Their numbers appeared smaller than in 2009, when 1 million or more people watched Obama’s first swearing-in. The best measure of the difference may have been ridership on Metro: As of 6 p.m., about 657,000 rides had been taken. At the same time four years ago, there had been 923,000.

Still, for many in the crowd, it was a moment whose magic was not dulled by repetition.

Sandra and Ronnie Robinson of Birmingham, Ala., set up folding chairs to watch the ceremony. Ronnie Robinson, 54, said he was in first grade in 1963 when white supremacists bombed the 16th Street Baptist Church in Birmingham. Four young girls were killed.

Attending Obama’s inauguration on the King holiday, 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 her first inauguration. Ward, who is African American, said she was serving in Iraq when Obama entered office.

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

Obama and Vice President Biden were, technically, on day two of their second term. Both had taken their oaths of office in private ceremonies on Sunday, to meet the constitutional date of Jan. 20. By tradition, when that date falls on a Sunday, the public ceremony is moved to the next day.

On Monday, Obama’s day began with a motorcade ride to the opposite side of Lafayette Square for a service at St. John’s Episcopal Church. The Old Testament reading was God’s advice to another leader with an ambitious agenda: Joshua, the successor to Moses.

“I hereby command you: Be strong and courageous; do not be frightened or dismayed, for the Lord your God is with you wherever you go.”

After a slow motorcade ride along Pennsylvania Avenue, the inaugural ceremonies began. There were appearances by pop-culture icons, both old and new: James Taylor sang “America the Beautiful,” Kelly Clarkson sang “My Country, ’Tis of Thee” and Beyoncésang the national anthem.

Latinos, a key part of Obama’s electoral coalition, occupied historic roles on the program. Supreme Court Justice Sonia Sotomayor, the daughter of Puerto Rican parents, administered the oath to Biden. Richard Blanco, the son of Cuban exiles, read the inaugural poem. Both were the first Latinos to perform either duty, and Blanco also was the first gay person in his role.

Blanco’s poem, “One Today,” was intended as a snapshot of a nation populated by hard workers and striving immigrants.

“Silver trucks, heavy with oil or paper, bricks or milk, teeming over highways, alongside us on our way to clean tables, read ledgers or save lives,” he read. “To teach geometry or ring up groceries, as my mother did for 20 years so I could write this poem for all of us today.”

For Obama, Monday’s inaugural address showed the evolution of a complicated political persona. In 2004, Obama became a national figure by telling his story as a second-generation American: his star-making speech at the Democratic National Convention began with the narrative of his father, who was born in Kenya.

By 2009, when Obama gave his first inaugural address, he spoke not as an inspirational symbol but as a national leader, counseling stoicism in the face of recession and suffering. “We must pick ourselves up, dust ourselves off and begin again the work of remaking America,” he said then.

On Monday, Obama cast himself in a third role: the face of a political agenda. Instead of merely holding the country together, he would seek to change it.

Here was a president freed — but also harried — by the knowledge that his clock was ticking, and he would never run for reelection again.

“We will respond to the threat of climate change, knowing that the failure to do so would betray our children and future generations,” he 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 did not explicitly mention gun control, a subject that seems certain to dominate the first months of his second term. But he did mention Newtown, Conn., where a shooting rampage last month spurred his recent push to tighten gun laws.

On immigration reform, Obama did not make specific new proposals. But he mentioned the topic, along with gay rights, among a series of struggles that sought to translate the Founders’ ambitions into modern times.

“Our journey is not complete until we find a better way to welcome the striving, hopeful immigrants who still see America as a land of opportunity,” he said, “until bright young students and engineers are enlisted in our workforce rather than expelled from our country.”

Now that Obama has articulated those goals, a serious fight remains. The House, and a powerful portion of the Senate, remains in the hands of Republicans — many of whom believe that Washington’s biggest problems are spending and debt.

On Monday, there already were signs that they viewed Obama’s agenda as, at best, a distraction from those pressing concerns.

Debbi Wilgoren and Rosalind S. Helderman contributed to this report.