An Islamic State video purporting to show the beheading of US hostage Steven Sotloff has sparked outrage.
UN Secretary General Ban Ki-moon said the act would be a "despicable crime".
The US is still trying to verify the video but said the killing if confirmed would be one of "sickening brutality".
His family said they were "grieving privately". Mr Sotloff, 31, was seized in Syria in 2013. He appeared in a video last month which showed fellow US journalist James Foley being killed.
A militant in the latest video also threatens to kill a British hostage, who is shown in the footage.
The family of the British hostage have asked the media not to release his name.
The militant has a voice with a British accent similar to that of the man who appeared to carry out the beheading of James Foley.
Prime Minister David Cameron is convening a meeting of the UK's Cobra emergency committee to discuss the matter.
After the news of the video emerged, US President Barack Obama ordered the deployment of another 350 troops to Baghdad to protect US diplomatic facilities.
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.
US state department spokeswoman Jen Psaki said the US was working to determine if the video was authentic.
She said: "If the video is genuine, we are sickened by this brutal act, taking the life of another innocent American citizen. Our hearts go out to the Sotloff family."
Ms Psaki said it was believed that "a few" other Americans were still being held by Islamic State.
Analysis: BBC security correspondent Frank Gardner
This second video from IS is significant, even though it was largely expected and dreaded. It shows that the recent US air strikes which have halted IS's lightning advance across northern Iraq are causing the organisation real damage, upsetting its plans to extend by force its rule into Kurdistan.
Unable to hit back militarily against America's jets, Islamic State has responded with a form of information warfare that it knows will horrify most people in the West.
Secondly, by threatening to murder a British hostage, IS shows it makes little or no distinction between the US and Britain as its enemy. This is despite Britain so far restricting itself to dropping aid to refugees and flying in supplies to the Kurdish military, leaving air strikes to the Americans.
Mr Ban, who is in New Zealand, said: "We are all outraged at reports from Iraq about the brutal killing of civilians by ISIL (IS), including yesterday's reported brutal beheading of another journalist.
"I strongly condemn all such despicable crimes and I refuse to accept that whole communities can be threatened by atrocity crimes because of who they are or what they believe."
Mr Cameron described the apparent beheading as an "absolutely disgusting, despicable act".
His office said he had known for months that a Briton was among the hostages. British officials say they have deliberately not commented and have "strong liaison" with relatives of the hostage.
Mr Sotloff was abducted near Aleppo in northern Syria in August 2013.
A spokesman for the Sotloff family 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."
One of Mr Sotloff's editors, Bill Roggio, of the Long War Journal, described him as an "extraordinary individual".
The video, entitled "A second message to America", is about two-and-a-half minutes long and was apparently recorded in a desert.
It appears to have been filmed after Mr Foley's, though it is impossible to determine the exact timing.
It shows a masked figure together with Mr Sotloff, who is dressed in an orange top and trousers.
Mr Sotloff reads out a text addressed to Mr 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 masked man describes the act he is about to commit as retribution for the US air strikes.
"I'm back, Obama, and I'm back because of your arrogant foreign policy towards the Islamic State... despite our serious warnings," the man says.
"We take this opportunity to warn those governments that enter this evil alliance of America against the Islamic State to back off and leave our people alone."