WEST DES MOINES, Iowa — When Pete Buttigieg was asked Thursday if it worried him that mostly white people attended his big rallies in South Carolina, he said yes.

But when Mr. Buttigieg, the former mayor of South Bend, Ind., was asked Saturday if he was concerned about speaking to a nearly all-white crowd in Storm Lake, a northwest Iowa town that is 38 percent Hispanic, he dodged the question.

While Mr. Buttigieg has established himself as a top-tier candidate in Iowa and New Hampshire, two states at the front of the Democratic presidential nominating calendar that are 90 percent white, he has struggled to win support from the black voters who make up the vast majority of the Democratic electorate in South Carolina, which comes fourth.

That has led Mr. Buttigieg to adopt divergent campaign styles for Iowa and for South Carolina.

In Iowa, Mr. Buttigieg is the centerpiece of his theater-in-the-round-style town hall events. The production is designed to show him as ascendant, with momentum building toward the state’s caucuses next Monday. In South Carolina, where the primary falls Feb. 29, Mr. Buttigieg still needs help telling his story, so he has invited prominent African-American supporters to interview him onstage, where he has faced sharper and more skeptical questions than he does in Iowa.