Admiral Lord West of Spithead said international intelligence was closing in on the masked man with a British accent believed to be responsible for the killings of US reporters Steven Soltoff and James Foley, who was murdered two weeks ago.
Speaking at a one-day conference at the Royal United Services Institute (Rusi) in London ahead of the Nato summit in Wales, the former head of the Royal Navy said he was confident the jihadist would be found and brought to justice soon.
Lord West said: “We probably know already who he is, we certainly will know soon.
“I would like to see him arraigned in the Hague for war crimes.
“He is a dead man walking, and he wants to think about that.”
The warning came as Foreign Secretary Philip Hammond confirmed that a preliminary analysis of a video purporting to show the beheading of Mr Sotloff suggested it was genuine.
Lord West went on to state that the Government should not rule out military action when dealing with the Islamic State extremists.
He said: “That is rather different from Isis and Isil. I refuse to call them the Islamic State because that gives them credibility. They clearly are happy to kill British citizens and we know they have said they want to destroy the British state.
“That is a different thing - that is why we have military forces.
“I’m not saying we should just go immediately and invade them, that would be stupid.” He added that military options should be part of the “overall planning”, along with diplomatic methods, interrupting money flows, and working with allies.
He said: “As part of that plan, if there are various targeted military things to be done, then they are not off the table.”
He said he was “sure” that the Government would be looking closely at possible military options to help “destroy this abhorrent group of people”.