He also indicated that UK officials were communicating with IS about the British hostage but again ruled out paying any ransom for his release.
"We need to show real resolve and determination, we need to use every power and everything in our armoury with our allies, with those on the ground, to make sure we do everything we can to squeeze this dreadful organisation out of existence," he told ITV news here.
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"I think it is very important that Western intervention isn't over the heads of those locally trying to fight this organisation and isn't done against the wishes and against the work of regional partners. That is sometimes the mistake that has been made in the past.
"The first thing we should do is help those on the ground fighting this organisation. Britain has been helping get arms to the Kurds and we are prepared to do more and we are considering actively whether to give them arms ourselves and whether we can do more directly to train Kurdish militia. We are already helping there, but we can do more," Cameron said.
The British premier also stressed that he is "absolutely certain" that the British-accented extremist responsible for the killings, referred to as "Jihadi John", will be caught and "one way or another face justice".
He conceded that the refusal to pay ransoms is "very difficult" for the families involved.
"I know it is difficult to hear and I've thought about this very carefully, but I'm absolutely convinced that the policy of not paying ransoms to terrorists for kidnaps is right," he said.
Cameron is attending a NATO summit in Wales where he will discuss a possible military intervention in Iraq with other world leaders.
IS has threatened to kill the British hostage, who reportedly has family based in Scotland, unless US air strikes on its positions in Iraq are halted.
The threat came in a video posted online on Tuesday showing the killing of US journalist Steven Sotloff.
IS had killed another US journalist, James Foley, last month and had demanded a $132 million ransom for his release.
The unnamed Briton was taken hostage in the village of Atmeh, in the Idlib province of north-west Syria, in March, 2013, along with an Italian aid worker and two Syrians, who have since been freed.
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