Pete Buttigieg pulled himself off the presidential campaign trail on Monday and returned to his day job as mayor of South Bend, Ind., after a police officer there shot and killed a black man.

“I know that whenever an incident like this happens, there is tremendous hurt that can come about,” Mr. Buttigieg said at a news conference on Sunday night.

The downshift from national campaigning comes at a time when Mr. Buttigieg has risen to the top tier of 2020 Democratic candidates. But he has struggled to win over African-American voters in early-voting states like South Carolina.

He presides over a midsize city with a large minority population, where his relations with African-American voters were damaged early in his tenure after he fired the city’s first black police chief. Mr. Buttigieg said the chief improperly handled recordings of police officers’ phone calls, a case that dragged through the courts for years.