Speaking to reporters in Number 10, PM Cameron said it seemed "increasingly likely" that a British citizen was the killer.
"Let me condemn the barbaric and brutal act that has taken place and let's be clear what this act is - it is an act of murder, and murder without any justification," he said.
"We have not identified the individual responsible, but from what we have seen it looks increasingly likely that it is a British citizen.
"This is deeply shocking. But we know that far too many British citizens have travelled to Iraq and travelled to Syria to take part in extremism and violence"