Josh Duggar holds his newborn son with wife Anna and the Duggar family in a past appearance on the Today Show.Today Show screenshot

The TLC network has pulled all episodes of the Duggar family reality TV programme following a report of child molestation claims against oldest son Josh Duggar.

Bizarrely, TLC was running a marathon of the 10-season series 19 Kids and Counting as the molestation reports surfaced in InTouch magazine. Josh Duggar, 27, has apologised for his "inappropriate behaviour" and has resigned from his position as executive director of the conservative lobbying group the Family Research Council in Washington DC.

Duggar was named in a police report as an "alleged offender" in an underage sex abuse probe years ago. He allegedly inappropriately touched five girls, including his sisters, sometimes while they were sleeping in the family home, beginning when he was 14 years old in 2002 and 2003. The incidents weren't reported until 2006 to investigators, who determined that it was too late under the statute of limitations to prosecute any of the alleged incidents, according to a reporter from the Northwest Arkansas Democrat-Gazette, who saw the now-sealed documents concerning the case.

"I acted inexcusably for which I am extremely sorry and deeply regret. I hurt others, including my family and close friends," said the married father of three on the family's Facebook page. "We spoke with authorities where I confessed my wrongdoing, and my parents arranged for me and those affected by my actions to receive counselling."

Parents Jim Bob and Michelle also expressed regret but said the difficulty also helped "each one of our family members" draw "closer to God".

The network hasn't made a final decision about the show's future, but has received a petition with close to 200,000 signatures demanding it be cancelled, reports TMZ. Advertiser General Mills has already informed the network that it is "blacklisting" the programme and has removed it from its advertising schedule.

Huckabee support for the Duggar family

TLC last year yanked its reality hillbilly show Here Comes Honey Boo Boo after family matriarch "Mama June" Shannon reportedly renewed a romantic relationship with an ex-lover and convicted child molester, whom one of her daughters accused of abusing her when she was eight. Shannon was furious TLC initially allowed the Duggar series to continue and threatened to sue the channel, reports the New York Daily News.

"I read that the Duggar family said this happening with their son brought them closer to God and each other," said Shannon. "So they're saying it's OK to have family touch time? Hell no."

But newly minted Republican presidential candidate Mike Huckabee is defending Duggar and the family.

"No purpose whatsoever is served by those who are now trying to discredit Josh or his family by sensationalising the story," the former governor said in a Facebook post Friday. "Good people make mistakes and do regrettable and even disgusting things."

The Duggars have endorsed Huckabee to be the GOP presidential candidate.