Prime Minister David Cameron has vowed that Britain will hunt down the killers of an aid worker beheaded by the Islamic State, which he described as the "embodiment of evil".
Cameron said on Sunday that Britain was prepared to "take whatever steps are necessary" after David Haines became the third Western hostage to be beheaded by the militants in less than a month.
IS released a video on Saturday showing Haines' killing and a death threat against another British captive, Alan Henning.
President Barack Obama offered US support for its "ally in grief".
A grim-faced Cameron said in a televised statement: "We will hunt down those responsible and bring them to justice, no matter how long it takes.
"Step by step we must drive back, dismantle and ultimately destroy ISIL (IS) and what is stands for. We will do so in a calm, deliberate way but with an iron determination.
"We will not do so on our own, but by working closely with our allies, not just the United States and in Europe, but with our allies in the region."
Cameron is facing growing pressure at home to take military action against IS, but he made no commitment to joining the US in launching air strikes on the group in northern Iraq and Syria.
US Secretary of State John Kerry was in Paris on Sunday to push for a broad international coalition against IS, which has already secured the backing of 10 Arab states.
The bid was boosted by Australia's announcement it was deploying 600 troops and 10 military aircraft to the United Arab Emirates to join the effort against what Prime Minister Tony Abbott called a "murderous death cult".
In France, President Francois Hollande's office said the "heinous killing" of Haines was another reason why a global push against IS was needed.
Obama slammed the killing of Haines as "barbaric" and said the US "stands shoulder to shoulder tonight with our close friend and ally in grief and resolve".
Haines, 44, who was taken hostage in Syria last year, had previously been shown alive in a video of US journalist Steven Sotloff's execution by IS militants earlier this month.
IS released a video claiming the execution of fellow US journalist James Foley on August 19.
The Foreign Office in London said the latest video released this weekend, entitled "A Message to the Allies of America", appeared genuine.
It opens with a clip of Cameron outlining how Britain was working with the Iraqi government to help arm Kurdish fighters against "these brutal extremist militants," and to offer aid, diplomacy, and military help to pressure IS.
Haines then appears, looking gaunt and dressed in an orange jumpsuit, and identifies himself, before calmly explaining that he is paying the price for Cameron's policy.
The attacker -- who appears to be the same man as in the previous two beheading videos -- tells Britain the alliance with the US will "accelerate your destruction" and will drag the British people into "another bloody and unwinnable war".
In a moving statement, Haines's brother Mike paid tribute to a man who was "most alive" when doing aid work. He had worked in conflict zones in the Balkans, Libya, South Sudan and Syria.
"He was, in the right mood, the life and soul of the party and on other times the most stubborn irritating pain in the ass," his brother said.
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