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COLUMBIA, S.C. — Senator Bernie Sanders spent Tuesday courting black voters in South Carolina with promises that he would combat institutional racism, reform police departments across the country, and make getting an education and a well-paying job easier.

Speaking to a group of religious leaders and students at a prayer breakfast at Allen University, a small historically black college here, Mr. Sanders stressed that he would transform an economy that has left many blacks behind.

Mr. Sanders then hosted a town-hall-style meeting at the University of South Carolina. He was accompanied by State Representative Justin T. Bamberg of South Carolina, the lawyer for the family of Walter L. Scott, who was fatally shot last year by a police officer in North Charleston, S.C.; and Erica Garner, the daughter of Eric Garner, who died in New York in 2014 after the police used a chokehold to subdue him.

Flanked by Ms. Garner and Mr. Bamberg, Mr. Sanders told the crowd of 300 mostly young white people that he wanted not only to overhaul the criminal justice system, but also make sure that police officers who break the law were held accountable.

“I’m tired of seeing videos, videos of Erica’s dad and other videos of unarmed people being killed by police officers,” Mr. Sanders said. “What is going on now, especially with regard to African-Americans — this is not new. It has been going on decade, after decade, after decade. The only difference is the cellphone video. That’s the only difference because what was going on in the past was never recorded and the police officer’s testimony was accepted as truth. This video, this cellphone, makes all the difference in the world. So clearly as a nation we need criminal justice reform.”

The senator also said he wanted to make sure that recidivism rates decrease and that people coming out of jails and prisons receive the job training needed to rebuild their lives. He also said that blacks in general need to be treated more fairly by the police, and he expressed disappointment in the way some police forces have systematically discriminated against blacks.

“We have got to achieve the day when young black males and women can walk the streets without worrying about being harassed by a police officer,” Mr. Sanders said. “I have talked to African-American Ph.D.s who get nervous when they have to travel or drive across the country. That should not be happening in the year 2016.”

He also pledged that if elected he would work to change things. “So count me in as somebody who if elected president will help lead the country in the fight against institutional racism and a broken criminal justice system,” Mr. Sanders said.

Mr. Sanders made his remarks as he and his rival, Hillary Clinton, are scrambling for black support heading into the Feb. 27 primary in South Carolina, where Mrs. Clinton holds a lead in polls but Mr. Sanders is working hard to gain ground. Mrs. Clinton was also giving a civil rights speech Tuesday, in Harlem.

Mr. Sanders said he believed he could win the Democratic primary here. “In South Carolina, I don’t know how far behind we started,” he said. “We have come a long way here in South Carolina. I think we are going to surprise people here.”

Earlier in the day, at Allen University, Mr. Sanders highlighted that a high percentage of black children live in poverty (he said 35 percent) and that an even higher percentage of young black people — 51 percent — were unemployed.

While delivering parts of his standard stump speech, Mr. Sanders also stressed that the “rigged economy” was leading him to focus on the plight of blacks and propose changes to improve their conditions.

“When we talk about inequality, it goes without saying that the African-American community is suffering even more,” Mr. Sanders told the crowd of 400 mostly black people. “And when we talk about what is going on in this country, and the fact that virtually the entire nation suffered terribly as a result of the greed and reckless and illegal behavior of Wall Street, which drove this economy into a terrible recession, the African-American community suffered more and has recovered in a much less significant way.”

Tuesday evening, Mr. Sanders planned to travel to Morehouse College in Atlanta as part of his tour of historically black colleges and universities.