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Donald J. Trump unleashed a torrent of insults on Thursday against his main rival, Ben Carson, comparing him to a child molester in a television interview and suggesting that the people of Iowa are “stupid” if they believe Mr. Carson’s claim that he tried to stab a close relative during his childhood.

The twin tirades came two days after the fourth Republican presidential debate, and as Mr. Carson has moved ahead of Mr. Trump in recent polls of Republican voters in Iowa, and in some national polls as well.

In an appearance in Fort Dodge, Iowa, Mr. Trump repeatedly laced into Mr. Carson and ranted that he was the lone seer who could solve what was wrong in the country.

His plan for the Islamic State? Mr. Trump said he would aggressively bomb the region, using a barnyard epithet to describe just how aggressively he would act and getting some applause from the crowd. “I would just bomb those suckers.”

It was a vastly different version of Mr. Trump than the one who seemed to be consciously trying to be more presidential on the debate stage. And it came as the debate over immigration, which has been his signature issue, was dominated by Senators Marco Rubio and Ted Cruz, threatening to crowd him out of the news media coverage that helped vault him to first place in the polls.

Mr. Carson has found himself under scrutiny over the veracity of some of the details of his life story, an inspirational tale of redemption that was the subject of his book, “Gifted Hands,” and which he has put at the forefront of his candidacy. During the debate this week, he faced one question from a moderator about the recent attention to his personal story, suggesting that people had “lied about” him and that he was the victim of a voracious press corps.

But Mr. Trump has been the only Republican in the large field of candidates to repeatedly criticize Mr. Carson and bring attention to the questions about his life. Yet at the debate, even as Mr. Carson stood a few feet away, Mr. Trump did not raise the issue. His attacks on Thursday, however, took on a new dimension.

In an interview with Erin Burnett on CNN, Mr. Trump repeated a previous criticism, saying that in “Gifted Hands,” Mr. Carson wrote that “he’s got a pathological temper. That’s a big problem, because you don’t cure that.”

He went on and suggested that some things cannot be cured. “As an example,” he said, “child molesting. You don’t cure these people. You don’t cure a child molester. There’s no cure for it. Pathological, there’s no cure for that.”

But, Mr. Trump insisted, he was simply bringing up what Mr. Carson himself had written.

“I’m not bringing up anything that’s not in his book,” he said. “You know, when he says he went after his mother and wanted to hit her in the head with a hammer, that bothers me. I mean, that’s pretty bad. When he says he’s pathological — and he says that in the book, I don’t say that — and again, I’m not saying anything, I’m not saying anything other than pathological is a very serious disease. And he said he’s pathological, somebody said he has pathological disease.”

Later, at the rally in Iowa, Mr. Trump, his voice dripping with disdain, mocked Mr. Carson’s claim about the attempted stabbing. In his telling, Mr. Carson says the knife struck the person’s belt buckle, sparing him a wound. Mr. Carson has previously described the person as a friend, but recently said it was a “close relative.”

With the crowd as quiet as a church congregation, Mr. Trump, on stage, acted out why he believed the story was not true.

“He took a knife and he went after a friend,” Mr. Trump said. “He lunged — he lunged that knife into the stomach of his friend. But, lo and behold, it hit the belt. It hit the belt, and the knife broke. Give me a break.”

Mr. Trump stepped away from the lectern to demonstrate why he said that scenario would not work, contorting his own belt buckle into different positions to show what would happen if someone had struck it with a sharp instrument.

“It ain’t going to be successful,” he said.

He called into the crowd, “Anybody have a knife, you want to try it on me?”

Yet in the case of Mr. Carson, he said, “amazingly, the belt stayed totally flat.”

“How stupid are the people of Iowa? How stupid are the people of the country to believe this crap?” he said.

An aide to Mr. Carson did not immediately respond to an email seeking comment.

Mr. Carson, a retired neurosurgeon, has forged a connection with evangelical voters, who make up a chunk of the Iowa caucus-going Republican electorate. Many have said they find his story of personal redemption through God inspiring, and his soft-spoken style appealing.

Mr. Trump, who has made his own success in opinion polls the crux of his campaign message, has sounded at times bewildered that Mr. Carson has moved ahead of him in the polls. “I don’t get it,” he said bluntly when Mr. Carson first overtook him, noting that his opponent does not travel to Iowa that frequently.