A family spokesman has said that Steven Sotloff's relatives are aware of the beheading video by the Islamic State (formerly known as Isis) and are in mourning, according to an AP report.
In a two-sentence statement, family spokesman Barak Barfi said Sotloff's family "knows of this horrific tragedy and is grieving privately."
The family has not been told whether the video is authentic, and Barfi said the family does not plan to make any additional comments at the moment.
In the video, a masked man describes the act he is committing as retribution for US air strikes. The executioner appears to be the same man who killed James Foley – known as 'Jihadi John' - and tells the camera: 'I'm back, Obama, and I'm back because of your arrogant foreign policy towards the Islamic State... despite our serious warnings."
"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 black-clad militant threatening to kill a captive, believed to be British hostage, David Haines.
US State Department spokeswoman Jen Psaki said: "If the video is genuine, we are sickened by this brutal act."
White House spokesman Josh Earnest said: "Our thoughts and prayers, first and foremost, are with Mr Sotloff and Mr Sotloff's family and those who worked with him."
He added that the US would be closely scrutinising the video. "If there is a video that's been released, 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".
Sotloff, of Florida, was abducted while reporting in Syria in 2013, sources told Checkpoint last month. He had reported from several other dangerous countries, including Yemen and Libya. He had worked for Time magazine, Foreign Policy and the Christian Science Monitor, and reported from Egypt, Libya and Syria.
The journalist 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 James Foley. Sotloff is shown at the end, as an Islamist militant gives the warning that his fate depends on President Obama's next move.
Foley's family released a statement after Sotloff's execution, calling it "just horrific," according to WHDH-TV.
On Thursday, Sotloff's mother Shirley Sotloff went on television to make a direct appeal for her son's life. She addressed Abu Bakr al-Baghdadi, the self-claimed caliph of Isis.
"My son is in your hands," Ms Sotloff said. "As a mother I ask Your Justice to be merciful and not punish my son for matters he has no control over. I ask you to use your authority to spare his life."
The SITE Intelligence Group, a U.S. terrorism watchdog, first reported about the video's existence. Unlike Foley's beheading, which was widely shared on Twitter accounts affiliated with the Islamic State group, the video purporting to show Sotloff's killing was not immediately posted online, though several jihadi websites told users to expect it on Tuesday.