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A US cable network has pulled a long running reality TV show following revelations of alleged sexual abuse by one of its members.

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.

Duggar has not admitted to the abuse but has apologised for his behaviour, saying he acted "inexcusably".

"I would do anything to go back to those teen years and take different actions," 27-year-old Duggar wrote in a statement on Facebook on Thursday.

"In my life today, I am so very thankful for God's grace, mercy and redemption."

TLC network said 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 Friday 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 Thursday 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 Mr Duggar's parents Jim Bob and Michelle Duggar, defended the family on Friday.

"Josh's actions when he was an underage teen are as he described them himself, 'inexcusable', but that doesn't mean 'unforgivable'," he wrote.