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COLUMBIA, S.C. — A plainly confident Hillary Clinton returned to South Carolina on Tuesday night for the first time since her victory in the Nevada caucuses and paid tribute to victims of gun violence and police misconduct as she campaigned before the state’s Democratic primary.

In a break with her monthslong strategy against Senator Bernie Sanders of Vermont, Mrs. Clinton did not criticize her rival or even refer to him obliquely as she reiterated her call for tougher gun laws, an issue that she usually uses to attack Mr. Sanders. She also spoke less about herself or her political needs than about the women who joined her in the church sanctuary: the mothers of the Black Lives Matter movement and former Representative Gabrielle Giffords of Arizona, who was nearly killed in a 2011 shooting and spoke haltingly and powerfully about her support for Mrs. Clinton.

As she heads into a series of Southern primaries that are likely to benefit her more than Mr. Sanders, Mrs. Clinton spoke forcefully about empathy for African-Americans who face disproportionately harsh treatment from the police and often begin their lives in poor school districts and lacking other advantages.

“White Americans, we need to do a better job when African-Americans talk about the seen and unseen barriers they face every single day,” Mrs. Clinton said. “We have to recognize our privilege and practice humility rather than assume our experiences are everyone’s experiences.”

That exhortation has recently become a central part of Mrs. Clinton’s stump speech as she courts black voters and tries to infuse her political message with more personal texture, such as emphasizing gratitude and humility. She has talked about those values in her own life, mainly in the context of her mother’s difficult upbringing. As she faced a growing political threat from Mr. Sanders, who has inspired voters with his denunciations of a “rigged” economic and political system, she reshaped her political message to try to inspire voters herself by espousing empathy and presenting herself as a problem-solver for strained or suffering Americans.

Introducing the women on stage and sharing the stories about the loss of their children, Mrs. Clinton drew an “amen” from the racially mixed audience as she said, “That’s too many deaths. Too many lives cut short.”

One by one, the mothers described their relationships to Mrs. Clinton in strongly personal terms, saying that she showered attention on them when they were deep in grief and continued to check in on them as they turned their mourning into a movement, as one of them put it.

“I endorse her because she endorsed us first,” said Gwen Carr, the mother of Eric Garner, who died in 2014 on Staten Island after New York City police officers put him in a chokehold after questioning him about selling loose cigarettes.

“I’m not angry enough to riot — I’m angry enough to vote for this lady,” said Geneva Reed-Veal, the mother of Sandra Bland, who died while in police custody in Texas last year after being pulled over for a traffic violation.

Ms. Reed-Veal drew laughter after she noted that Mrs. Clinton had not put the mothers up to campaigning for her in South Carolina this week.

“There are no payments being made, there are no secret emails about this,” Ms. Reed-Veal said, perhaps inadvertently reminding people about the controversy over Mrs. Clinton’s use of a private email server as secretary of state.

Ms. Giffords, the last to address the audience, drew a standing ovation as she called Mrs. Clinton “courageous” and said she would “stand up to the gun lobby” as president.

“Speaking is difficult for me, but come January, I want to say these two words: madam president,” Ms. Giffords said.

Mrs. Clinton has a strong lead over Mr. Sanders in polls ahead of the Saturday primary here, and they will compete again in 11 Super Tuesday primaries and caucuses on Tuesday. Super Tuesday will provide 880 delegates, the biggest trove on any single day of the nomination fight. They are vying to accumulate the 2,383 delegates needed to clinch the nomination. Mrs. Clinton has a slight lead over Mr. Sanders in pledged delegates — the sort that come from winning states, like the 880 at stake on Tuesday — and a large lead in superdelegates, who count toward the nomination and can shift their allegiance anytime. Mrs. Clinton is poised to add substantially more pledged delegates to her column over the next several weeks, with Sanders advisers acknowledging that the coming primaries were favorable for Mrs. Clinton and put Mr. Sanders in a mathematical bind in the delegate race.

