"I can assure you that we will look at every possible option to protect this person," foreign secretary Philip Hammond said after an emergency government meeting held on the eve of a two-day summit of NATO leaders in Wales.
Cameron chaired the meeting, which was called after the release on Tuesday of a video showing the execution of a second US journalist by Islamist fighters in Iraq.
"A country like ours will not be cowed," Cameron said, adding: "We will not waver in our aim of defeating terrorism".
In a video showing the severed head of 31-year-old Steven Sotloff, a masked militant warned that a British man, widely identified as David Cawthorne Haines, would be killed in response to US air strikes against militants in northern Iraq.
Britain and the US have both authenticated the recording.
The militant spoke English with a British accent similar to that of the alleged killer of journalist James Foley in a video released by Islamic State extremists last month.
"We will look very carefully at the options available to us to support the legitimate government of Iraq and Kurdistan in defending themselves," Hammond said.
"If we judge that air strikes could be beneficial, could be the best way to do that, then we will certainly consider them but we have made no decision to do so at the moment.
"We have to deal with ISIS on the basis of the wider threat that they pose to the British public as well as this individual," he said.
- Fighters 'speak for no religion' -
Speaking on Tuesday, Cameron condemned Sotloff's beheading as "a despicable and barbaric murder".
"ISIL terrorists speak for no religion," Cameron said.
Britain has so far not joined in US air strikes against the Islamist fighters, but has helped arm Kurds fighting in northern Iraq and has dropped aid to people surrounded by IS fighters on Mount Sinjar and in the town of Amerli.
Earlier this week, however, Cameron implied he could order air strikes without prior approval from parliament -- something the government failed to get last year when it was considering retaliation for the use of chemical weapons in Syria.
Cameron said he would keep parliament "permanently updated".
"If, however, something needed to be done urgently to protect a particular British national interest or to prevent some humanitarian catastrophe, it might be necessary to act and then come to parliament," he said on Monday.
"We have to make a judgment about how we best help those on the ground, and to date that judgment has been to provide aid and political support and to help with certain military aspects.
"The Americans have gone further and provided air strikes. I think that is the right way to approach this problem," he said.
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