Condemning the "barbaric" beheading of a second US hostage by Islamic State extremists, Cameron told MPs that "this country will never give in to terrorism and our opposition to Isil (IS) will continue at home and abroad".
"What has happened to the two hostages so far and what may happen again in the future is utterly abhorrent and barbaric and these people need to understand we will not waver in our aim of defeating terrorism," he said while speaking at Prime Minister's Questions.
An IS video posted online two weeks ago showed the killing of another US journalist, James Foley.
Sotloff, 31, who was seized in Syria last year, also appeared in that footage with a warning that he would be next.
The British hostage appears at the end of the latest video, released yesterday and entitled 'A Second Message To America'. The US has confirmed the video is authentic.
Cameron told the House of Commons: "A country like ours will not be cowed by these barbaric killers. If they think we will weaken in the face of their threats, they are wrong.
He said Britain would continue with its policy of not paying ransoms - which is also the US policy - as such payments funded the promotion of terrorism.
Concurring with Cameron, Labour leader Ed Miliband said: "Events like this must strengthen, not weaken, our resolve to defeat them and he can be assured of our full support in standing firm against them."
British Foreign Secretary Philip Hammond earlier said the UK will look at "every possible option" to protect the British hostage.
Speaking after a meeting of the Cobra emergency committee, Hammond said: "I can assure you we will look at every possible option to protect this person."
Media here reported that the person in the video has family in Scotland but relatives do not want him named.
The Islamic State has thrived and mutated during the civil war in Syria. It swept into Iraq in June, seizing large swaths of the country's Sunni-dominated northern and western provinces.
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