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 compared Islamic State (IS), the group which made a video of Mr Foley's killing, to a "cancer" and said its ideology was "bankrupt".
IS said Mr Foley's death was revenge for US air strikes on its fighters in Iraq.
But Mr Obama pledged to continue "to do what we must do" to confront IS.
The UN, UK and others have also expressed abhorrence at the video.
Mr Foley's mother Diane said he "gave his life trying to expose the world to the suffering of the Syrian people".
The Foleys have not watched the video of their son's death, but James' father John said he was appalled by how his son died.
"It haunts me, how much pain he was in," Mr Foley told reporters.
James Foley, 40, 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".
In the video, Mr Foley is shown next to a masked man with a British accent, and Prime Minister David Cameron said he was shocked that a British citizen looked likely to be involved in the killing.
'A message to America'
A grim-looking Mr Obama said IS militants had "no place in the 21st Century".
"No just god would stand for what they did yesterday or what they do every single day," he added.
He said the future would be won by those such as James Foley, who "built rather than destroyed".
In the IS 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 delivers a warning to the US government: "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.
UK Prime Minister David Cameron has condemned the killing as "deeply shocking" but said it was "not a time for a knee-jerk reaction".
UN Secretary-General Ban Ki-moon called it "an abominable crime that underscores the campaign of terror".
Earlier, French President Francois Hollande told Le Monde: "I think we are in the most serious international situation since 2001" - the year of the 11 September attacks in the US.
Analysis: BBC Security Correspondent Frank Gardner
Shocking as it is, the video of James Foley being beheaded by a masked jihadist is not without precedent.
In 2004 al-Qaeda's offshoot in Iraq, led by Abu Musab Al-Zarqawi, the forerunners of Islamic State (IS), did the same thing to Nick Berg, a hapless American telecoms engineer who fell into their clutches.
The group went on to murder Briton Ken Bigley in the same way, after first getting him to plead on camera with the then Prime Minister Tony Blair to change Britain's course in Iraq.
These grisly murder videos are abhorrent to most Muslims and non-Muslims alike and they've even been discouraged by Osama Bin Laden's successor as a "vote loser".
But for the hard-core jihadists of IS they serve a number of purposes: to horrify and scare their enemies, to boost the morale of their own by showing the impotence of the West to prevent it, and thereby to embarrass the US and Britain, with the hope of making them temper their military actions in Iraq.
Mr Foley had spent many years reporting from the world's trouble spots.
He covered the war in Libya and was detained there for more than 40 days.
"I'm drawn to the drama of the conflict and trying to expose untold stories," he told the BBC in 2012.
"There's extreme violence, but there's a will to find who these people really are. And I think that's what's really inspiring about it."
Mr Foley's mother Diane, writing on Facebook, urged the militants to free any other hostages.
"Like Jim, they are innocents. They have no control over American government policy in Iraq, Syria or anywhere in the world," she wrote.
The US launched air strikes almost a fortnight ago, in an attempt to help Kurdish forces curb the advance of Islamic State militants in northern Iraq and recapture the Mosul dam, the biggest in Iraq.
IS has been accused of massacring hundreds of people in areas under its control in Iraq and also in eastern Syria.
- Formed out of al-Qaeda in Iraq (AQI) in 2013, IS captured Raqqa in eastern Syria
- By early 2014 it controlled Falluja in western Iraq
- It has since captured broad swathes of Iraq, seizing Mosul in the north in June and the Mosul dam in August
- The violence has displaced an estimated 1.2 million people in Iraq alone
- Pursuing an extreme form of Sunni Islam, IS has persecuted non-Muslims such as Yazidis and Christians, as well as Shia Muslims, whom it regards as heretics
- In July alone, IS expanded dramatically, recruiting some 6,300 new fighters largely in Raqqa, an activist monitoring group said