On the day that he was originally set to return to his hometown and receive the sentence for his 34 felony convictions, former President Donald J. Trump found himself a few miles east, basking in the raucous adulation of a packed arena on Long Island.

Standing in front of thousands at the Nassau Coliseum in Uniondale, N.Y., Mr. Trump received a local hero’s reception, as he drew an exaggerated depiction of a New York in decline, made false claims and hammered Democrats over crime, inflation and immigration.

He continued to falsely maintain that Springfield, Ohio, had been over overrun by illegal immigrants, even though the Haitian community he was referring to has temporary legal status. Then, he announced he would visit both that city and Aurora, Colo., another focal point of his exaggerated claims about migrants.

“I’m going to go there in the next two weeks. I’m going to Springfield, and I’m going to Aurora,” Mr. Trump said. “You may never see me again, but that’s OK. Got to do what I got to do.”

As he discussed Springfield, members of the crowd began chanting, “Save the cats,” a reference to a debunked claim spread by Mr. Trump that Haitian migrants were abducting and eating pets. (Springfield’s Republican mayor said this week that a visit from Mr. Trump would burden the city’s strained resources.)

Mr. Trump’s rally on Long Island was his second campaign event since the apparent assassination attempt against him on Sunday in West Palm Beach, Fla. Though he spoke with typical vigor about the incident, he later appeared jumpy at one point, as someone apparently approached the stage.

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