The conspiracy theorist Alex Jones hemmed and hawed when pressed repeatedly by Megyn Kelly to admit he was wrong to call the massacre at Newtown, Connecticut, a hoax.

Jones did not give a direct answer in a segment on NBC’s Sunday Night with Megyn Kelly. Kelly has been criticized for giving a platform to Jones, who has also called the 9/11 attacks an inside job and promoted the false story that a pizza restaurant in Washington DC was the site of a child sex ring.

She has defended her decision by noting that Jones’s influence has grown with the rise of President Donald Trump, who has praised him and appeared on his radio program.

“Here’s the thing, Alex Jones isn’t going away,” she said on Sunday night.

The Infowars host said at one point he was playing “devil’s advocate” in denying the 2012 mass shooting at the Sandy Hook elementary school. But he added that he remained skeptical after he “watched the footage” of children leaving the building.

“Some of it looks like it’s real but then what do you do when they’ve got the kids going in circles in and out of the building with their hands up,” he said. “I’ve watched the footage. That looks like a drill.”

The segment with Jones combined Kelly’s interview with background providing his history of false remarks, his relationship with Trump and comments from a Newtown parent Neil Heslin, whose six-year-old son, Jesse Lewis, was killed in the shooting. When Kelly asked Heslin whether he had anything to say to Jones for Father’s Day, he responded: “I think he’s blessed to have his children to spend the day with, to speak to. I don’t have that.”

Last week Jones leaked an audio recording of what he said was a phone conversation with Kelly, heard promising she would not portray him as “some kind of bogeyman”. Shortly before Sunday’s night interview, Jones released a Father’s Day video in which he offered condolences to families who had lost children in the “horrible tragedy” of Newtown but did not refer to his previous comments disputing the killings.

“Parents should never have to bury their own children,” Jones said.

Connecticut’s NBC affiliate said on Friday it wouldn’t air the report. In an internal memo obtained by the Associated Press, NBC Connecticut staff members were told station executives had made the decision after listening to concerns from employees, Sandy Hook families and viewers, and considering “the deep emotions from the wounds of that day that have yet to heal”.

Lawyers who represent 12 people who lost loved ones at Sandy Hook urged NBC News officials not to air the interview. The NBC News chairman, Andy Lack, said the Jones story would be edited with its critics in mind.

The interview was seen as a test of the interviewing skills of Kelly, the former Fox News star whose questions two weeks ago for Vladimir Putin were widely panned for being too easy on the Russian leader. An unaired segment obtained by the Huffington Post showed Kelly telling him that “virtually every person we have met on the street says what they respect about you is they feel that you have returned dignity to Russia”.

Kelly challenged Jones from the start, introducing him as a “radical conspiracy theorist” and promising to confront him for his “notorious lie” about Sandy Hook. The two frequently interrupted each other as Kelly kept asking if he would admit to his wrongdoing and a visibly tense Jones kept deflecting her questions, blaming the media for distorting his remarks or veering between acknowledging and disputing the tragedy.

“I will sit there on the air and look at every position and play devil’s advocate,” he said.

Answered Kelly: “Of course, there is no evidence on the other side.”

Jones also downplayed his connection to Trump, who has spoken warmly of him and at times seemed to use conspiracies aired on Infowars in his campaign speeches.

“I think my influence on Trump is way, way lower than what MSM [mainstream media] has said,” he said, adding that he and the president were “friendly” but not friends.

After spending more than a decade at Fox, Kelly signed a multimillion-dollar contract with NBC this year. Her star power grew after she challenged Trump during a 2015 Republican debate on his history of sexist remarks and the candidate responded with a series of angry tweets and other comments, sometimes crude and personal, and boycotted a later debate because she was one of the moderators.

She was a key figure in the downfall of the former Fox News chief Roger Ailes, telling in-house investigators of inappropriate conduct by Ailes that supported Gretchen Carlson and other women who had made similar accusations. Kelly wrote of her battles with Trump and Ailes in her bestselling 2016 memoir, Settle for More.

Kelly’s old employer needled her at the weekend, sending a tweet headlined “Megyn Kelly and Alex Jones: NBC News under fire for ‘botched’ rollout.”