“No, I never, never would,” Mr. Trump responded from the stage.

After Mr. Trump finished speaking, one woman in the crowd followed the candidate off the stage, according to the pool reports, repeatedly asking him what he meant by “you have nothing to lose,” a line the candidate has said repeatedly in his efforts to attract minority voters.

Before his trip to the church, Mr. Trump spent roughly 15 minutes getting a brief tour of a water treatment plant in Flint, according to pool reports, where he thanked managers in the same town that had its water poisoned. “It’s not an easy situation, but you’ll get it under control,” Mr. Trump told the small gathering of employees and officials. He thanked “the folks from Flint” and in particular the “really, really good executives.”

Mr. Trump spoke of his visit to Flint at a campaign rally later on Wednesday in Canton, Ohio, saying the water crisis in Flint “demonstrates failure in every single level of government,” and repeatedly pointing to the automobile jobs that fled the city decades ago. “It used to be cars were made in Flint and you couldn’t drink the water in Mexico,” Mr. Trump told the crowd, repeating a line he said earlier in the day. “Now, the cars are made in Mexico and you can’t drink the water in Flint. Oh, I hate to say that, but it’s true, it’s true, it’s true.”

The candidate’s swing through Flint, a town with a majority African-American population, follows his campaign’s recent outreach to minorities elsewhere and Mr. Trump’s visits to states where Republicans haven’t won Electoral College votes in decades. The last time Michigan voted for a Republican was in 1988, and most recent polls there have shown Mrs. Clinton maintaining a comfortable lead over Mr. Trump.