An Islamic State video has appeared which purports to show the beheading of Steven Sotloff, a US journalist being held hostage by the militants.
Mr Sotloff, 31, was abducted in Syria in 2013. He appeared at the end of 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.
Mr Sotloff’s family said they were aware of the video and were “grieving privately”.
After Mr Foley’s death, Mr Sotloff’s mother appealed to IS leader Abu Bakr al-Baghdadi to save her son’s life.
White House spokesman Josh Earnest said US officials were checking the reports.
The US has recently carried out dozens of air strikes against IS targets in Iraq.
President Barack Obama has ordered the deployment of another 350 troops to Baghdad to protect US diplomatic facilities, the White house has said.
Analysis: BBC security correspondent Frank Gardner
This second execution 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.
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 gown.
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, whose voice is similar to that of the man who appeared to carry out the beheading of James Foley, then 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.”
The video ends with the militant threatening to kill the British captive.
US state department spokeswoman Jen Psaki said: “If the video is genuine, we are sickened by this brutal act.”
Mr Earnest urged caution about the veracity of the video.
“Our thoughts and prayers, first and foremost, are with Mr Sotloff and Mr Sotloff’s family and those who worked with him,” he said.
“I’m not in a position to confirm the authenticity of that video or the reports.
“It’s something that will be analysed very carefully by the US government and our intelligence officials to establish its authenticity.”
UK Prime Minister David Cameron described the apparent beheading as an “absolutely disgusting, despicable act”.
Mr Cameron’s office said he has known for months that a Briton was among the hostages taken by Islamic State and has chaired meetings with high-level officials to discuss the situation.
But British officials say they have deliberately not commented on this while there has been what they call “strong family liaison” with relatives of the hostage.
A friend of Mr Sotloff, US film maker Matthew Van Dyke, told the BBC: “He was a complete professional and there was no reason for this to happen to him.”
Mr Sotloff was abducted near Aleppo in northern Syria in August 2013.
He had worked for Time magazine, Foreign Policy and the Christian Science Monitor, and reported from Egypt, Libya and Syria.
Time Magazine editor Nancy Gibbs said in a statement that she was “shocked and deeply saddened by reports of Steven Sotloff’s death”.
“He gave his life so readers would have access to information from some of the most dangerous places in the world,” she said.
Friends said he had lived in Yemen for many years and spoke good Arabic.
At the time of his capture, his family chose not to go public with details, on the advice of officials.
Last month a video was released showing the beheading of Mr Foley.
Mr Sotloff was shown at the end, as a militant gave a warning that his fate depended on President Obama’s next move.
The US has launched more than 120 air strikes in Iraq in the last month, in an attempt to help Kurdish forces curb the advance of Islamic State militants and protect minorities threatened by them.