“Shame on you,” wrote Cristina Hassinger, the daughter of Dawn Hochsprung, who was the school’s principal.
Ms. Kelly said on Twitter that the point of the interview was to “shed a light” on Mr. Jones, especially because President Trump had been a guest on Mr. Jones’s show. When Mr. Trump, then a Republican presidential candidate, appeared on the show in 2015, he told Mr. Jones: “Your reputation is amazing. I will not let you down. You will be very, very impressed, I hope. And I think we’ll be speaking a lot.”
Ms. Kelly, also noting that Infowars had been given a White House press credential, said many people may be unfamiliar with Mr. Jones.
She posted a preview of the interview on her Twitter account. In it, she asked Mr. Jones: “They call you the most paranoid man in America. Is that true?” Ms. Kelly said.
“Absolutely not,” said Mr. Jones. “A paranoid person would be hiding out in their house, not venturing out in public. I go out there on the street and battle Black Lives Matter, the Communists, point-blank range.”
She then gives cues to Mr. Jones, prompting him to repeat some of the most prominent conspiracy theories he has touted.
“9/11,” Ms. Kelly says.
“Now 9/11 was an inside job, but when I say inside job it means criminal elements in our government working with Saudi Arabia and others, wanting to frame Iraq for it,” Mr. Jones replies.
“Sandy Hook,” she says.
“Well Sandy Hook’s complex because I have had debates where, we devil’s advocates have said the whole story is true, and then I have had debates where I have said, that none of it is true.”
Ms. Kelly then asked him: “When you say parents faked their children’s death, people get very angry.”
“Well I know, but they don’t get angry about the half million dead Iraqis from the sanctions, or they don’t get angry about … ” Mr. Jones said, before he is interrupted by Ms. Kelly, who says, “That’s a dodge.”
“No it’s not a dodge,” he continued. He said he “looked at all the angles of Newtown, and I made my statements long before the media even picked up on it. We didn’t get any of the real important stuff.”
“Well here’s the big one they always make fun of me. You probably want to throw this in there. Thirty years ago, they began creating animal-human hybrids. Isn’t that the big story Megyn Kelly should be doing?” Mr. Jones said.
A spokesman for NBC did not immediately reply to an email seeking comment.
In a segment on Infowars on Monday, Mr. Jones called on NBC to not broadcast the interview.
“They did not have me in there saying that I believed children died at Sandy Hook,” Mr. Jones said about the preview, claiming that he was misled by Ms. Kelly and that it was edited to misrepresent him.
Six educators and 20 first-grade students were shot dead by Adam Lanza on Dec. 14, 2012, at the Newtown, Conn., elementary school. Mr. Lanza, 20, who had also killed his mother earlier that morning, then turned the gun on himself.
Parents of the Newtown victims have been harassed and threatened by conspiracy theorists, who accuse them of fabricating the massacre. This month, a Florida woman was sentenced to prison for issuing death threats to one Newtown family.
Ms. Hassinger, who said in a telephone interview that she would not watch the program, said her family has been bombarded with requests for evidence that her mother was killed.
“We have been harassed repeatedly by people who we call hoaxers that think this hasn’t happened. When there is going to be such a widely available interview with attention given to one of the hoaxer ringleaders, it is going to unleash the trolls on us tenfold all over again.”
Some people on social media called for a boycott of the program and the network, and some shared information about the advertisers for the program.
On Facebook, a page dedicated to the memory of a slain teacher, Victoria Soto, 27, addressed a post to Ms. Kelly and the network: “Alex and his followers have done nothing but make our lives a living hell for the last 4½ years,” it said. “This incessant need for ratings at the cost of the emotional well-being of our family is disgusting and disappointing.”
An earlier version of this article misidentified the state with a yogurt factory owned by a Kurdish immigrant. It is Idaho, not Iowa.