The interview, scheduled to air on Wednesday, comes about two weeks after the start of the backlash following reports of inappropriate conduct between the Duggars' eldest son, Josh, and minors when he was a teenager.
"Kelly will speak with the parents about their son’s molestation allegations and the controversy surrounding their family right now," Fox News Channel said in a news release Saturday. "Additional portions of the interview, which will take place at the Duggar home in Arkansas, will air during a one-hour 'Kelly File' special on Friday, June 5."
"The Kelly File" averages 2.5 million viewers. Fox News Channel, owned by 21st Century Fox, is available in more than 90 million homes.
Josh Duggar, 27, resigned his post as executive director for FRC Action, the lobbying arm of conservative Christian group Family Research Council, the day the allegations surfaced. He then issued an apology on a post on his family's Facebook page.
The scandal ignited on social media, where many expressed anger and disappointment toward the Arkansas family featured on the show using the hashtags #CancelTheDuggars, #DitchTheDuggars and #BoycottTLC.
Streaming giant Hulu severed ties with TLC's "19 Kids and Counting" last week. Companies such as Walgreens, Payless Shoe Source, Choice Hotels, Pure Leaf Iced Tea and General Mills said they plan on removing their ads from the show.
The Duggars have also become been a frequent topic among presidential hopefuls. Republican presidential candidate Rick Santorum told ABC News' Chief Anchor George Stephanopoulos last week that he was "sickened" by the allegations.
Though TLC said that it was yanking repeats of "19 Kids and Counting" from its schedule, it has yet to cancel the show. TLC did not immediately reply for comment.
The channel was launched in 1972 as the Appalachian Community Service Network. It became the Learning Channel in 1980. TLC is available in about 94 million homes in the U.S. It is the second-most widely viewed channel owned by Discovery Communications, behind the Discovery Channel. From late September to early May, TLC, whose target audience is women, averaged more than 1 million viewers a night during prime-time hours, according to Nielsen.
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