SOUTH BEND, Ind. — Mayor Pete Buttigieg took a third day off from the campaign trail on Wednesday to confront a crisis over the fatal police shooting of a black resident of South Bend, Ind. Mr. Buttigieg said he was “extremely frustrated” that the white officer’s body camera was switched off at the time.

The shooting of the 54-year-old man revived longstanding mistrust by some black residents of the city police and of Mr. Buttigieg, and it has presented the mayor, a Democratic presidential candidate, with a national leadership test just a week before the first primary debates.

The case has revived scrutiny of Mr. Buttigieg’s history of sometimes strained relations with African-Americans in South Bend. The issue is echoing in the Democratic primary as Mr. Buttigieg, 37, seeks to improve his support with black voters.

[18 questions. 21 Democrats. Here’s what they said.]

After addressing a half-dozen newly sworn-in officers — all white — on Wednesday morning, Mr. Buttigieg, the son of two Notre Dame professors, acknowledged to reporters outside police headquarters that he had only a “theoretical” understanding of the charged issue of race and policing when he took office nearly eight years ago.