Businessman Donald Trump cast Ben Carson as “low energy” and “very, very weak” on immigration and trade negotiations in a round of interviews Sunday, a response to poll numbers that showed him trailing the retired neurosurgeon in the key early-voting state of Iowa.

Mr. Trump appeared chastened and confused by the numbers, although it didn’t stop him from making insinuations about Mr. Carson’s religion and slapping him with dismissive labels that he has used on another Republican presidential rival, former Florida Gov. Jeb Bush.

“Actually, I think Ben Carson is lower energy than Jeb, if you want to know the truth,” Mr. Trump told CNN.

In response, Mr. Carson said he is not about to dive into the “mud pit” of political sniping. He said anyone who can operate on someone for 20 hours straight has demonstrated the type of stamina that the presidency demands.

The exchange is the latest sign of discord between a pair of unlikely front-runners, who have mostly avoided direct combat as they ride a wave of enthusiasm for political outsiders.

Mr. Carson received the support of 28 percent of likely participants in the Iowa Republican caucuses in the Bloomberg Politics/Des Moines Register numbers released Friday. Mr. Trump was at 19 percent — down four percentage points since August.

A Quinnipiac University poll released Thursday also showed Mr. Carson overtaking Mr. Trump in the state and leading by 8 points, 28 percent to 20 percent.

“I don’t understand the poll; I actually don’t,” Mr. Trump told CNN about the Bloomberg/Des Moines Register survey.

Sen. Ted Cruz of Texas was third in that poll at 10 percent, followed by Sen. Marco Rubio of Florida at 9 percent. Former Florida Gov. Jeb Bush and Sen. Rand Paul of Kentucky trailed at 5 percent apiece, followed by former Hewlett-Packard CEO Carly Fiorina at 4 percent and former Arkansas Gov. Mike Huckabee at 3 percent.

Mr. Trump joked that people tried to tell Mr. Carson about the Iowa results but he appeared to be sleeping.

Mr. Carson said he was a volatile person in his youth and may be relaxed and soft-spoken now, but he plans to stay above the fray.

“That’s not who I am. And I don’t get into the mud pit. And I’m not going to be talking about people,” Mr. Carson said. “I will tell you in terms of energy I’m not sure that there’s anybody else running who’s spent 18 or 20 hours intently operating on somebody.”

The former surgeon then carved through a series of prominent Republican issues with NBC host Chuck Todd, defending his suggestion that an armed populace might have resisted Nazis in Germany.

“I think it is generally agreed that it’s much more difficult to dominate people who are armed than people who are not armed. You know, some people will try to take that and, you know, make it into an anti-Jewish thing, which is foolishness,” he said.

He also said the 1973 Supreme Court decision in Roe v. Wade, which established abortion as a national right, should be overturned, leaving the door open to exceptions in cases in which the life of the mother is at risk, but not for rape or incest.

As the doctor surges in Iowa, the businessman is stirring the pot so evangelicals wonder whether Mr. Carson, a member of the Seventh-day Adventist Church, is a true Christian.

Mr. Trump, a Presbyterian, refused to apologize Sunday, saying he was only curious about Mr. Carson’s denomination.

“All I said was, I don’t know about it,” he told ABC’s “This Week,” though he refused to explain why he brought it up in the first place.

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