“When I hear him saying he’s not sure he’s going to respect the results of the election, it makes me think of the period of dictatorship in the Dominican Republic when politicians didn’t respect the will of the people,” said Nieves Padilla, 60, an organizer with Make the Road Action, a New York-based immigrant advocacy group, who came to the United States in 1975.

Few would go so far as to predict mass violence or coups d’état if Mr. Trump lost and refused to concede, given the country’s loyalty to the rule of law.

But it was precisely America’s reputation as a role model for democracy that made the candidate’s comments so jarring for some naturalized citizens. In their minds, they said, questions about a president’s legitimacy were inseparable from chaos and bloodshed, and thus they could not stop themselves from thinking the worst.

“He said, ‘I will concede only if I win?’ My goodness,” said Cristina Drost, 82, a retired teacher in Henderson, Nev. She said she immigrated from the Philippines in 1961 after her uncle, while running for Congress there, was shot by people who did not think he should be in the race. (He survived.) “It is encouraging his supporters who could do some drastic things like killing, especially today since people have guns,” she said of Mr. Trump’s comments.