Mr. Trump is not the only person pointing to what he considers to be the troubling consequences of immigration to Sweden. This month, a seasoned investigator with the police department in Orebro, Peter Springare, caused a stir with a Facebook posting in which he discussed the case files on his desk.

“What I’ve been handling Monday-Friday this week: Rape, rape, serious rape, assault rape, black mail, black mail, assault in court, threats, attack against police, threats against police, drugs, serious drugs, attempted murder, rape again, black mail again and abuse,” Mr. Springare said. He went on to list the first names of the people he said were suspects, all but one of which were traditionally Middle Eastern.

The post, which was shared 20,500 times, led to an outpouring of support. People sent hundreds of flowers to Mr. Springare’s police station, and more than 170,000 people joined a Facebook group supporting him.

But both his superiors and the police in other departments said that they did not recognize his description, and that national levels did not resemble his claims.

Manne Gerell, a lecturer in criminology with Malmo University, said more immigrants than Swedes commit crimes, but the exact numbers are hard to determine. And on the national level, he said, the imbalance is not nearly as great as Mr. Springare suggested.

Still, it seems as if frustrations over the issue are spreading.

In 2014, the anti-immigrant Sweden Democrats gained 12.9 percent of the vote in parliamentary elections to become the country’s third-largest party, up from only 2.9 percent eight years earlier.