Prime Minister David Cameron vowed Sunday that Britain would hunt down the killers of an aid worker beheaded by the Islamic State, which he described as the "embodiment of evil".
Cameron said 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 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."
- 'Murderous death cult' -
Cameron is facing growing pressure at home to take military action against IS, but he made no commitment to joining the United States in launching air strikes on the group in northern Iraq and Syria.
Britain began sending weapons this week to Kurdish fighters battling the militants in northern Iraq, but has faced accusations of confusion over its strategy.
US Secretary of State John Kerry was in Paris Sunday to push for a broad international coalition against IS that has already secured the backing of 10 Arab states including Saudi Arabia.
The bid was boosted by Australia's announcement that it was deploying 600 troops to the United Arab Emirates to join the effort against what Prime Minister Tony Abbott called a "murderous death cult".
France is hosting an international conference on Iraq on Monday, and President Francois Hollande's office said the "heinous killing" of Haines was another reason why a global push against IS was needed.
Signup to our newsletter and follow us on Facebook and Twitter!
A European Union foreign policy spokesman called the murder "another demonstration of ISIL's determination to pursue and extend its terror strategy, in breach of all universally recognised values and rights".
Obama slammed the killing as "barbaric" and said the US "stands shoulder to shoulder tonight with our close friend and ally in grief and resolve".
- 'A good brother' -
Haines, 44, who was taken hostage in Syria last year, had previously been shown alive in the video of US journalist Steven Sotloff's killing.
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".
At the end of the clip, the militant threatens to execute Henning, another captive Briton.
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.
Haines's Croatian wife Dragana was keeping a low profile at their home in the quiet Croatian town of Sisak.
They have a four-year-old daughter, Athea, while Haines has a teenage daughter from his first marriage to his childhood sweetheart in Britain.
Obama has set out a strategy that would include air strikes in Syria and expanded operations in Iraq, where US aircraft have carried out more than 160 strikes since early August.
On Sunday, his national security adviser Denis McDonough told NBC's Meet the Press success will come when IS no longer poses a threat to the United States and its allies in the Middle East.