DAVENPORT, Iowa — Nearly every time a politician has dared to offer him censure, Donald J. Trump has responded by tagging his adversary with an impish nickname. In Mr. Trump’s world, Ted Cruz became “Lyin’ Ted,” Marco Rubio was “Little Marco,” and Hillary Clinton remains “Crooked Hillary.”

At a pair of rallies in Iowa on Thursday, Mr. Trump seemed to confer a new term of non-endearment, referring with great disdain to a certain “very little guy.”

“I was going to hit one guy in particular, a very little guy,” he told a crowd of supporters in Davenport. “I was going to hit this guy so hard his head would spin, he wouldn’t know what the hell happened.”

Although this particular object of Mr. Trump’s disaffection went unnamed, he seemed to be referring to Michael R. Bloomberg. The two have traded barbs for months. In February, Mr. Trump urged Mr. Bloomberg, the former New York City mayor, to run for president as an independent because he would “beat him.”