Kat Redding, a Sanders supporter, invoked a fatal shooting this year of a black resident of South Bend by a white police officer. “When it comes to holding police accountable, Mayor Pete is not a man of action,” she told the crowd.

Perceptions of Mr. Buttigieg among black voters nationally — he polls in the low single digits among them — have been shaped by wide news coverage of the police shooting in June. It exposed a history of distrust of police by some black residents. That is not a phenomenon unique to South Bend — a city with a famous university, Notre Dame, but also many poor and working-class residents. African-Americans make up 26 percent of the population, and the local black poverty rate is almost twice the national rate. In a presidential debate, Mr. Buttigieg acknowledged he had failed to increase diversity on the police force.

But Mr. Buttigieg’s record over eight years also includes many initiatives that backers of the mayor here say benefited minority residents.

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“The narrative for so long now for South Bend has been that there’s no blacks in support of the mayor,” said Ms. McBride, who traveled as a surrogate for Mr. Buttigieg in South Carolina and helped organize the South Bend gathering last week for local black leaders who support the mayor. Although the Buttigieg campaign promoted the event, the speakers said it was their idea.

Among them were two council members and three pastors, including Michael Patton, the president of the local N.A.A.C.P. chapter. “Pete is someone who has done significant work in our community,” Mr. Patton said.

He and the others ticked off initiatives under Mr. Buttigieg: a small-business resource center on the West Side where minority residents are concentrated; the hiring of the city’s first diversity officer; legal help for tenants facing evictions; and funding for home repairs in historically marginalized neighborhoods.