There are others vying for these voters’ attention. Senator Elizabeth Warren of Massachusetts was in the Mississippi Delta earlier this month talking about affordable housing. Senator Amy Klobuchar was in Florida, touting how she had been discussing 2020 strategy with Andrew Gillum, the African-American candidate who narrowly lost the Florida governor’s race in November. Senator Cory Booker of New Jersey has been a near-constant Southern presence the last couple of years, offering his endorsement and oratorical skills to a range of Democratic candidates.

This activity is a demonstration of the belief among 2020 contenders that the hearts and minds of black female voters are up for grabs in the Democratic primaries. Strong potential suitors are still weighing presidential bids, including former Vice President Joseph R. Biden Jr. and Stacey Abrams, the popular black Democrat from Georgia. For now, Ms. Harris, 54, is one of two major black Democratic candidates — along with Mr. Booker — and many southern black and liberal voters are excited by the idea of the first black woman president.

While Ms. Harris has drawn enthusiastic audiences, she has also faced some criticism that as a former prosecutor and California attorney general, parts of her criminal justice record were insufficiently progressive. And Ms. Harris, whose father is from Jamaica and whose mother is from India, has been the target of offensive online memes about her race that have sparked questions among some voters.

On Sunday, as Ms. Harris prepared to introduce herself at Atlanta’s Ebenezer Baptist Church, a former New York state corrections officer named Lamarr Robinson brought up both matters. He criticized Ms. Harris’s handling of a highly-publicized case of a black death-row inmate whose case was tainted by racism. And Mr. Robinson added, “She’s more east Indian than African-American.”