A day after former President Donald J. Trump, in a debate watched by millions, doubled down on his campaign’s debunked position that immigrants are eating people’s pets in Springfield, Ohio, a local official on Wednesday pushed back on the outlandish claim.

Bryan Heck, the city manager in Springfield, said in a taped statement that it was “disappointing” that the narrative about the city had been “skewed by misinformation circulating on social media and further amplified by political rhetoric in the current, highly charged presidential election cycle.”

Officials with the City of Springfield, which has had an influx of Haitian immigrants in recent years, have said that there are no credible reports of immigrants’ harming pets. Mr. Heck said the new residents have brought challenges but also benefits — helping local businesses and the city’s broader economy, and spurring housing development not seen in the city in decades. The new arrivals have also put pressure on the community’s schools and hospitals.

But on the debate stage in Philadelphia on Tuesday night, Mr. Trump spoke of immigrants in Springfield “eating the dogs” and “eating the cats” — claims rooted in viral social media posts.

“They’re eating the pets of the people that live there,” he said.

The bizarre assertion has put a global spotlight on Springfield, a blue-collar city of some 60,000 people between Dayton and Columbus.

Even Germany’s Foreign Office on Wednesday, while pushing back on a claim that Mr. Trump had made about the country giving up on ambitious renewable energy efforts, mocked the pet-eating remarks.