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LITTLE ROCK — Donald J. Trump, back in fighting form, told a record crowd here Wednesday night that he believes he won the Iowa caucuses.

“Actually, I think I came in first,” he told a cheering crowd of more than 11,500 people who packed into Barton Coliseum to hear him.

Mr. Trump, who placed second in Iowa, was continuing a theme he had been unspooling over the previous 24 hours — that in his view, Senator Ted Cruz, who won Monday’s caucuses, had in fact stolen the election.

Mr. Cruz was declared the winner, with 27.6 percent of the vote; Mr. Trump came in second, with 24.3 percent.

At various sites throughout the day, including on Twitter and Boston Herald Radio, Mr. Trump said that the Cruz campaign had deceitfully told voters Monday night that Ben Carson had dropped out of the race, with the expectation, Mr. Trump said, that Carson supporters would turn to Mr. Cruz.

The Carson campaign has also accused the Cruz campaign of dirty tricks. (Mr. Carson had not dropped out; he was skipping New Hampshire and going home, his campaign said, for a change of clothes.)

Mr. Trump said Wednesday that the caucuses should be nullified and Iowa should hold its caucuses all over again. He might even file a complaint or sue to nullify the results, he said. By his calculation, that makes him the winner.

Mr. Cruz has said that Mr. Trump “finds it very hard to lose” and has been mocking him and his “Trumper tantrums.”

“We’re liable to wake up one morning and Donald, if he were president, would have nuked Denmark,” Mr. Cruz told a crowd in New Hampshire on Wednesday. “That’s not the temperament of a leader to keep this country safe.”

Mr. Trump seemed to have been knocked off his game temporarily after the Iowa caucuses. While the polls in New Hampshire show him with a big lead over his Republican rivals, he has hesitated to talk about winning. But by Wednesday night in Little Rock, he had come roaring back.

“I think we’re going to do great in New Hampshire,” he said.

At the rally, which began nearly two hours late, Mr. Trump excoriated Mr. Cruz as a “flat-out liar.” And he blamed Mr. Cruz for the Affordable Care Act, because he had supported Chief Justice John Roberts on the Supreme Court and he voted to uphold the plan.

Mr. Trump even took questions from the audience, which he rarely does and certainly not in a vast arena. One young man asked him how he would get rid of gun-free zones.

“Gun-free zones are a disaster,” Mr. Trump pronounced. “It’s like holding up candy to a baby. It’s like saying, ‘Please come and kill us because we have absolutely no protection.’ ”

Meanwhile, his staff has been busy adding events to his calendar. He is planning five in New Hampshire on Thursday, including a town hall event in Exeter at noon.