US President Barack Obama has said the beheading of US journalist James Foley is "an act of violence that shocks the conscience of the entire world".
Mr Obama said the ideology of Islamic State, the group which made a video of Mr Foley's killing, was "bankrupt" and would ultimately fail.
IS said Mr Foley's death was revenge for US air strikes on its fighters in Iraq, according to the BBC. The United Nations, Britain and others have expressed abhorrence at the video.
American warplanes have continued to strike IS targets in Iraq, as Mr Obama vowed that the US would do what it must to protect its citizens.
James Foley's mother Diane said he "gave his life trying to expose the world to the suffering of the Syrian people".
The 40-year-old had reported extensively across the Middle East, working for US publication GlobalPost and other media outlets including French news agency AFP. In a statement, GlobalPost asked for "prayers for Jim and his family."
French journalist Nicolas Hénin was held in captivity with Mr Foley for seven months before being freed in April this year. He said Mr Foley had been maltreated in captivity yet kept his sense of identity.
A grim-looking Barack Obama said the US would continue to do "what is necessary" in the fight against IS militants, and described them as "a cancer", saying they had "no place in the 21st century. No just god would stand for what they did yesterday or what they do every single day."
Mr Obama said the future would be won by those such as James Foley, who built rather than destroyed.
UN Secretary-General Ban Ki-moon called the beheading "an abominable crime that underscores the campaign of terror".
French President Francois Hollande told Le Monde newspaper: "I think we are in the most serious international situation since 2001" - the year of the 11 September attacks in the US.
'Message to America'
In the Islamic State video, titled A Message to America, a man identified as James Foley is dressed in an orange jumpsuit, kneeling in desert-like terrain beside an armed man dressed in black.
He gives a message to his family and links his imminent death to the US government's bombing campaign of IS targets in Iraq.
Clearly under duress, he says: "I call on my friends, family and loved ones to rise up against my real killers, the US government, for what will happen to me is only a result of their complacency and criminality."
Then the masked militant, who speaks with a British accent, delivers a warning to the US government: "You are no longer fighting an insurgency. We are an Islamic army and a state that has been accepted by a large number of Muslims worldwide.
"So any attempt by you Obama to deny the Muslims their rights of living in safety under the Islamic caliphate will result in the bloodshed of your people."
After he speaks, the militant appears to start cutting at his captive's neck before the video fades to black. His body is then seen on the ground.
Another captive, identified as American journalist Steven Sotloff, is shown at the end, with the warning that his fate depends on President Obama's next move. Mr Sotloff was abducted in northern Syria a year ago, the BBC reports.
Britian trying to identify executioner
Britain's Prime Minister David Cameron condemned the killing as "deeply shocking" but said it was "not a time for a knee-jerk reaction".
Mr Cameron later said it was likely the man who beheaded James Foley was a British citizen, and British intelligence was working to identify the masked militant.
He said far too many British citizens had travelled to Syria and Iraq to join the fighting and he promised to redouble his efforts to stop more people going.
Intelligence workers are trawling through databases, that they know of, of the approximately 500 British jihadists who have gone out to Syria and looking at their Facebook postings, Twitter and other social media postings and communications, the BBC reports.
They will also be mapping audio files to see if there's any recognition from the masked militant's voice anywhere else and talking to people who have been held prisoner in Syria by other jihadists.