Former President Donald J. Trump escalated the nativist, anti-immigration rhetoric that has animated his political career with a speech Friday in Aurora, Colo., where he repeated false and grossly exaggerated claims about undocumented immigrants that local Republican officials have refuted.

For weeks, Aurora has been fending off false rumors about the city. And its conservative Republican mayor, Mike Coffman, said in a statement on Friday that he hoped to show Mr. Trump that Aurora was “a considerably safe city.”

But Mr. Trump has made debunked claims about Aurora, a Denver suburb, such a central part of his stump speech that he took a campaign detour to Colorado, which has not voted for a Republican in a presidential election since 2004, to make the case in person at a rally at the Gaylord Rockies Resort & Convention Center.

And during a meandering 80-minute speech Mr. Trump repeated claims, which have been debunked by local officials, that Aurora had been “invaded and conquered,” described the United States as an “occupied state,” called for the death penalty “for any migrant that kills an American citizen” and revived a promise to use the Alien Enemies Act of 1798 to deport suspected members of drug cartels and criminal gangs without due process.

That law allows for the summary deportation of people from nations with which the United States is at war, that have invaded the United States or that have engaged in “predatory incursions.” It was far from clear whether the law could be used in the way that Mr. Trump was proposing.

The false tale that Aurora, Colorado’s third-largest city, was occupied by armed Venezuelans stemmed from a dispute over housing conditions.

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