David Cameron and Barack Obama have vowed to confront the militant group Islamic State (IS).
In a joint article in The Times (£), the leaders said the UK and US could "not be cowed by barbaric killers", claiming those who want to adopt an "isolationist approach" do not understand the threat faced.
"Developments in other parts of the world, particularly in Iraq and Syria, threaten our security at home," they wrote.
"We will not waver in our determination to confront Isil. If terrorists think we will weaken in the face of their threats they could not be more wrong.
"Countries like Britain and America will not be cowed by barbaric killers."
The western leaders were speaking ahead of a two-day Nato summit in Newport which will begin later today.
I've been told at the Nato summit that the intelligence services know exactly who 'Jihadi John' is - or at least are 99.9% certain.
The British aid worker being held by Islamic State is David Haines, a 44-year-old father-of-two from Perth, Scotland.
In a video statement which claims to record his final words US hostage and journalist Steven Sotloff blames US foreign policy for his death.