Gen. David Richards told the BBC Sunday that it was not possible to destroy an idea such as radical Islam and that it was vital to ensure that good government and development existed to counteract it.
""I don't think you can probably defeat an idea, it's something we need to battle back against as necessary, but in its milder forms why shouldn't they be allowed to have that sort of philosophy underpinning their lives," Richards said.
Richards, a former NATO commander in Afghanistan, became chief of Britain's defense staff last month. He said the notion of al-Qaida and other militant groups continuing to exist was not a new idea.
Shadow defense secretary Jim Murphy told the BBC he agreed there was probably no purely military solution to militant Islam.
"I think he's right to talk about the different ways that this has got to be taken on -- militarily yes but diplomatically and in a peaceful sense of nation building in Afghanistan is also important," Murphy said.