ROUND O, S.C. — While Pete Buttigieg sat in a semicircle with six entrepreneurs at a black-owned winery, a rooster crowed nearby, its cock-a-doodle-dooing drowning out the South Bend, Ind., mayor’s explanation of how he would help small-business owners of color.

This wasn’t the Mayor Pete phenomenon that’s taken Iowa by storm.

Following stinging criticism about his lack of support from Democrats of color, Mr. Buttigieg this week embarked on a four-day, three-state tour across the South. Rather than play to high school gymnasiums packed with adoring crowds as he’s done in Iowa, where staff members have led crowds in choreographed dance moves, Mr. Buttigieg appeared in austere settings in North Carolina, South Carolina and Alabama that were more typical of an unknown candidate’s first appearances on the presidential campaign trail.

For a candidate who has risen from obscurity to the top-tier of the Democratic field thanks to his ubiquity on television and social media, the campaign swing served as a first overture to black audiences who have received far less attention from his campaign than a largely white cohort of donors and Iowa caucusgoers. The trip was engineered to introduce him to black voters — and perhaps just as importantly, to show him being introduced to black voters.

“We certainly knew that there was an opportunity and a need to mix it up in terms of our style of engagement and our approach,” Mr. Buttigieg said during an interview Tuesday in Okatie, S.C. “When you’re reaching out to voters who don’t yet feel that they know you, and you’re reaching out to parts of the electorate that have often felt taken for granted or overlooked by the regular political process in a lot of ways, it’s important to have that two-way conversation.”