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BIRMINGHAM, Ala. — Thousands of people packed into an auditorium here on Monday night for a Martin Luther King Day rally held by Senator Bernie Sanders that at times felt like a boisterous football game.

After pointedly debating Hillary Clinton on Sunday, Mr. Sanders seemed more energized than ever as he engaged with people in the crowd who shouted his name, loudly applauded at his policy ideas and booed at mentions of Mrs. Clinton and Republican presidential candidates. The Vermont senator’s hourlong speech focused on the legacy of the Rev. Dr. Martin Luther King Jr. and on how his presidency would continue Dr. King’s legacy by fighting various forms of discrimination and inequality.

“It is absolutely imperative that we see his life not as a museum piece, something simply to be looked at, to be studied, to be appreciated, to be kept on a shelf,” Mr. Sanders said of Dr. King. “To truly honor the life of Dr. King, we must fight to carry out his radical and bold vision for America. And his vision was of a nation in which we not only end all forms of institutional racism, and bigotry, but a nation in which all of us, black, and white, and Latino, Asian-American, Native American, all of us, come to together to create a country which provides economic, social and environmental justice for all.”

Mr. Sanders also spoke about other core issues of his campaign, including the need to break up big commercial banks, to reform campaign finance laws, to increase the minimum wage to $15 an hour, to invest in sustainable energy and to transform wealth distribution. He talked of recently released details about his plan to create a “single-payer Medicare for all” health care system, and of his plans to use taxes on the rich to pay for progressive programs. And, riding the high of his debate performance, Mr. Sanders reminded the crowd that he is close to beating Mrs. Clinton in Iowa and New Hampshire.

About 5,700 people were at the event at Boutwell Auditorium, and another 1,400 people outside watched it from an overflow area on large televisions.

Earlier in the day, Mr. Sanders visited the 16th Street Baptist Church, where four black girls were killed in a bombing in 1963. “This was terrorism,” he said during the tour.

He also stopped by the Birmingham Civil Rights Institute, where he touched the bars of the Birmingham jail cell where Dr. King was held and viewed exhibits including segregated water fountains and a Ku Klux Klan robe.

Before the event, people eager to get into the auditorium braved frigid weather and stood for more than an hour in a line that extended blocks and wrapped into a nearby parking lot. As the event’s start time neared, volunteers bellowed that the space was filling up fast and was standing room only.

“The end of the line is all the way down,” a volunteer shouted to people who looked shocked at the turnout. One supporter sighed, dismayed by the wait. Another, however, cheerfully stared at the line and declared, “This gives me hope.”

Chris Echols, 41, drove about 90 miles from his home in Montgomery to see Mr. Sanders. As he stood in line, Mr. Echols said that until Sunday’s debate he had been undecided about which Democratic candidate to support.

Now, he plans to vote for Mr. Sanders. Mr. Echols also said that if Mrs. Clinton were to win the Democratic nomination and Mr. Sanders were to run as an independent, he would still vote for Mr. Sanders.

“The biggest thing for me is health care,” Mr. Echols, an audio-visual technician, said. “He finally laid out how he is going to pay for it, and he kind of stood his ground on a lot of issues. I think before now I looked at him like he was just a cranky old guy going on and on about the same things.”

As the event came to a close, Mr. Sanders said he would have to work hard to win Alabama’s March 1 primary. He added that those in the crowd had harder work to do in the Southern state to garner support than he had to do in Vermont. In the end, he left them with a direct message.

“We have got to go out to our white, working-class friends,” Mr. Sanders said to the mostly white crowd. “We have got to go out to our brothers and sisters there and say stop voting against your own best interests.”