The series 19 Kids and Counting on TLC stars a conservative Christian couple and their 19 children.
It has been alleged that the eldest son Josh Duggar molested five underage girls as a teenager.
Josh Duggar, 27, has not admitted to the abuse but has apologized for his behavior, saying he acted “inexcusably”.
He wrote in a statement on Facebook on May 21: “I would do anything to go back to those teen years and take different actions.
“In my life today, I am so very thankful for God’s grace, mercy and redemption.”
TLC network also said in a statement that it was “deeply saddened and troubled by this heartbreaking situation”.
“Our thoughts and prayers are with the family and victims at this difficult time,” the statement said.
Arkansas police said on May 22 they had received a court order to destroy records of a nearly decade-old investigation into Josh Duggar. No charges were filed against him.
Police concluded the statute of limitations had passed, according to the Northwest Arkansas Democrat-Gazette newspaper.
On May 21, Josh Duggar resigned his role with a prominent conservative Christian group amid reports about the allegations.
Republican presidential candidate Mike Huckabee, who has been supported by Josh Duggar’s parents Jim Bob and Michelle Duggar, defended the family on his Facebook page on May 22, saying: “Josh’s actions when he was an underage teen are as he described them himself, <<inexcusable>>, but that doesn’t mean <<unforgivable>>.”
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