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MEMPHIS —A day after black voters delivered Hillary Clinton an overwhelming victory in the South Carolina primary, she spoke at two black churches here, vowing to “tackle the continuing challenge of systemic racism” and denouncing the leading Republican candidate’s ubiquitous slogan.

“America has never stopped being great,” she said at the Greater Imani Cathedral of Faith, her allusion to Donald J. Trump prompting a loud amen. “Our task,” Mrs. Clinton continued, “is to make America whole.”

Mrs. Clinton’s drop-ins on Sunday services, where many congregants were dressed in traditional African garb to celebrate the final days of Black History Month, earned her warm welcomes and standing ovations.

After capturing nearly 74 percent of the black vote in South Carolina, Mrs. Clinton hopes that deep reservoir of support will propel her to victories against Senator Bernie Sanders in Tennessee, Georgia, Alabama and other Southern states that have Democratic contests on Tuesday.

But the church visits also provided Mrs. Clinton with a general election contrast with Mr. Trump, who spent his Sunday morning fielding questions about David Duke, the white nationalist and former Ku Klux Klansman, after Mr. Duke told a radio audience that voting against Mr. Trump was “treason to your heritage.”

After Mr. Trump, in a CNN interview, repeatedly declined to disavow Mr. Duke’s support, Mr. Sanders posted a message on Twitter, which Mrs. Clinton quickly seconded: “The first black president cannot and will not be succeeded by a hatemonger who refuses to condemn the KKK.”

Mr. Trump faced criticism from his Republican rivals as well, and posted on Twitter later in the day, “As I stated at the press conference on Friday regarding David Duke- I disavow.”

Mrs. Clinton did not mention Mr. Trump by name on Sunday, but she has begun sounding a theme of bringing more “love and kindness” to the country.

“I know it’s kind of odd sometimes when people hear me talking about, as I did last night in South Carolina, how we need more love and kindness,” she told the Mississippi Boulevard Christian Church.

“But I believe that with all my heart,” she said. “We have to start treating each other with respect, listening to each other, holding out hands, a fellowship to make sure we know we believe we are all in this together.”

Mrs. Clinton spent Sunday afternoon in Nashville, greeting voters and picking up a latte in the city’s funky Hillsboro Village neighborhood before visiting historically black Meharry Medical College. She was to wind up a long day of campaigning with a late-night rally in Pine Bluff, Ark.

In her stump speech, Mrs. Clinton seemed to put Mr. Sanders in her rear-view mirror, turning instead to a focus on the broad stakes in the election if a Republican were to win in the fall. “I’m looking forward, if I’m so fortunate to be the nominee, to debating any one of them,” she said of the Republican candidates.

She also spoke about the countries she visited as secretary of state — “large ones, small ones, itsy bitsy ones,” she said at a stop in Nashville.

“They all want to be like us,” she said. “I believe that America is great, right now — what we need is to be whole, we need to be whole where everybody feels like we’re all in this together.”

A man in the crowd yelled out, “We love you, Hillary!”

Mrs. Clinton smiled and said, “You know, I’m all about love and kindness, so I sure appreciate that.”

