The Press Association said a planned trip to a frontline base in the volatile Helmand province on Thursday did not go ahead after mobile phone calls referring to a possible rocket attack on a helicopter were intercepted.
A senior Afghan Taliban commander based in Helmand and a spokesman for the militants told NBC News that they had made all arrangements to kill Cameron and had even deployed a separate "commando squad" of Taliban fighters for this "important task."
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They said they knew when the British leader arrived in Kabul that he would go to meet his troops in Helmand, NBC News said.
"The task to hit a chopper that was supposed to carry the British prime minister was given to our commando squad, specially trained for such kind of missions," the Taliban commander, who did not wish to be named, told NBC.
"Even missiles were installed in various places from where we could hit his chopper," he added.
The commander said they were unable to carry out their "mission" when the trip was canceled.
Taliban spokesman Zabihullah Mujahid also made similar claims and said Cameron was "lucky."