President Barack Obama has vowed the US will not be intimidated, after Islamic State militants released a video showing the beheading of American journalist Steven Sotloff.
Mr Obama warned: “Our reach is long and justice will be served.”
Another US journalist, James Foley, was similarly murdered last month.
Separately, the UK held a meeting of its emergency Cobra committee after threats to kill a British hostage who was also shown in the latest video.
‘They have failed’
US National Security Council spokesperson Caitlin Hayden said that US intelligence agents had “analysed the recently released video showing US citizen Steven Sotloff and has reached the judgment that it is authentic”.
Speaking in Estonia, Mr Obama said the beheading was a “horrific act of violence and we cannot begin to imagine the agony everyone who loves Steven is feeling right now. Our country grieves with them”.
He added: “Whatever these murderers think they will achieve by killing innocent Americans like Steven, they have already failed.
“They have failed because, like people round the world, Americans are repulsed by their barbarism. We will not be intimidated. Their horrific acts only unite us as a country and stiffen our resolve.
“Those who make the mistake of harming Americans will learn that we will not forget, that our reach is long and that justice will be served.”
Mr Obama said the US strategy was to “try to ensure Isil is not an ongoing threat to the region”. Islamic State is also often referred to as Isil or Isis.
But Mr Obama warned such a strategy would take time and effort.
UK Prime Minister David Cameron told MPs the two American beheadings were “utterly abhorrent and barbaric”, adding: “We will not waver in our aim of defeating terrorism.”
Foreign Secretary Philip Hammond said: “We are doing everything we can to reassure the family of the British hostage who was shown in the video.”
A spokesman for the Sotloff family had earlier indicated they believed the video was genuine, issuing a statement that said: “The family knows of this horrific tragedy and is grieving privately. There will be no public comment from the family during this difficult time.”
US state department spokeswoman Jen Psaki said it was believed that “a few” other Americans were still being held by Islamic State.
‘I’m back, Obama’
Mr Sotloff, 31, who also held Israeli citizenship, was abducted in northern Syria in August 2013.
He had appeared in a video last month which showed James Foley being killed.
The latest video, entitled “A second message to America”, is about two-and-a-half minutes long and was apparently recorded in a desert.
Next to a masked figure, Mr Sotloff reads out a text addressed to President Obama saying: “You’ve spent billions of US taxpayers’ dollars and we have lost thousands of our troops in our previous fighting against the Islamic State, so where is the people’s interest in reigniting this war?”
The militant spoke with a British accent similar to that of the man who appeared to carry out the beheading of James Foley.
Mr Hammond told the BBC it seemed to be the same person.
The man says: “I’m back, Obama, and I’m back because of your arrogant foreign policy towards the Islamic State… despite our serious warnings.”
He also threatens to kill the British hostage shown in the footage. The family of the British hostage have asked the media not to release his name.
Islamic State has seized large swathes of territory in Iraq and Syria in recent months, declaring a new caliphate, or Islamic state, under leader Abu Bakr al-Baghdadi.
The US has launched more than 120 air strikes in the past month to try to help Kurdish forces curb the IS advance.
After the latest video emerged, Mr Obama ordered the deployment of another 350 troops to Baghdad to protect US diplomatic facilities.