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Queen Elizabeth's grandson is in Afghanistan on a four-month tour, based in Camp Bastion in the volatile Helmand province, where he will be on the front line in the NATO-led war against Taliban insurgents.
"We are using all our strength to get rid of him, either by killing or kidnapping," Zabihullah Mujahid, a Taliban spokesman, told Reuters by phone from an undisclosed location.
"We have informed our commanders in Helmand to do whatever they can to eliminate him," Mujahid added, declining to go into detail on what he called the "Harry operations".
NATO Secretary-General Anders Fogh Rasmussen said he was not worried about the Taliban threat against Prince Harry.
"That's not a matter of concern," Rasmussen told a news conference in Brussels on Monday. "I mean, we do everything we can to protect all our troops deployed to Afghanistan whatever might be their personal background."
Britain's Ministry of Defence declined to comment on Mujahid's statement. British authorities have given few details of Prince Harry's stint in Afghanistan for security reasons.
The 27-year-old prince, who is third in line to the throne, took up his new role two weeks after being photographed frolicking naked in Las Vegas.
Known in the military as Captain Wales, he first served in Afghanistan in 2008 as an on-the-ground air controller, but his tour was cut short when a news blackout designed to protect him while he was on the front line collapsed.