When the head of a local gun group tried to present Donald J. Trump with a lifetime membership card at a campaign event on Sunday in Cincinnati, Mr. Trump asked the man to toss it to him over a phalanx of guards, not wanting an unfamiliar member of the crowd to get too close.

Earlier in the day, at a rally in Illinois, Mr. Trump hoped to invite a Hispanic supporter from the audience to join him onstage and say a few words. But first he asked his security personnel if they would allow it.

“He knows if he makes a move, he’s going to get clobbered by these guys,” Mr. Trump said, offering something of a warning to anyone who would do him harm.