Families of some of the 26 people who were killed in the 2012 Sandy Hook Elementary School massacre have criticized an upcoming NBC interview with Alex Jones, the conspiracy theorist who has said the shooting was a hoax perpetrated by forces hostile to the Second Amendment.

As the host of “The Alex Jones Show” and the operator of the right-wing website Infowars, Mr. Jones has a wide following. He has called the Sept. 11, 2001, attacks in New York City an inside job, promoted and then later apologized for helping spread the hoax known as “Pizzagate,” and asserted that an Idaho yogurt factory owned by a Kurdish immigrant was associated with a sexual assault before retracting that claim amid a lawsuit.

Now, Mr. Jones will have a new platform.

Megyn Kelly, who left Fox News earlier this year to anchor a new weekly show for NBC, “Sunday Night With Megyn Kelly,” said on Sunday that she would air an interview with Mr. Jones on June 18 “to discuss controversies and conspiracies.”