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The elite troops said they will not rest until they “capture or kill” the blood-thirsty jihadists who have beheaded four western hostages in six weeks.

Mr Henning is believed to have been killed on Friday when a video of his ­execution was put on the internet.

Muslims around the world had called for him to be released but were ignored by the Islamic State terrorist group. His death has prompted ­international condemnation.

The masked killer thought to be ­responsible for his beheading was the British terrorist known as Jihadi John, inset.

Last night one senior SAS source described the killer as a “dead man walking”.

The source said: “Rest assured we will get this bastard – that is for certain. He is at the top of our kill list.

“There is real anger and frustration among ­the ­regiment that we were unable to save Alan. He was a good, decent man who didn’t deserve to die like that.” Members of the crack unit who returned from ­operations in Iraq last week say they are ­“frustrated” with politicians for their “confused strategy” in Iraq and Syria.

Several SAS men have complained they had “no idea what the strategy was”.

Others said their role in Iraq was constrained and they were denied the opportunity to directly attack IS.

The SAS’ primarily role is to establish “ground truth”, the military term to find out what is happening in northern Iraq and where the IS ­fighters are based. They are also calling in air strikes against IS compounds and vehicle convoys, conducting battle damage assessment after air attacks and training the Kurdish Peshmerga guerrillas.

One source said: “The SAS wants to avenge Alan Henning’s death. They were desperate to try and rescue the hostages but neither the US nor the British have been able to get the right intelligence.

“We are trying to fight a very dirty war with one hand tied behind our backs and the terrorists know it. It’s time for the shackles to come off.”

The SAS and the US Delta Force are now in a race against time to rescue American hostage Peter Kassig.