BEIRUT — Islamic State extremists released a video Tuesday purportedly showing the beheading of a second American journalist, Steven Sotloff, and warning President Barack Obama that as long as U.S. airstrikes against the militant group continue, “our knife will continue to strike the necks of your people.”

The footage — depicting what the U.S. said appeared to be a sickening act of brutality — was posted two weeks after the release of video showing the killing of James Foley and just days after Sotloff’s mother pleaded for his life.

Barak Barfi, a spokesman for the family, said that the Sotloffs had seen the video but that authorities have not established its authenticity.

“The family knows of this horrific tragedy and is grieving privately. There will be no public comment from the family during this difficult time,” Barfi said.

Sotloff, a 31-year-old Miami-area native who freelanced for Time and Foreign Policy magazines, vanished in Syria in August 2013 and was not seen again until he appeared in a video released last month that showed Foley’s beheading.

Dressed in an orange jumpsuit, Sotloff was threatened in that video with death unless the U.S. stopped airstrikes on the Islamic State.

In the video distributed Tuesday and titled “A Second Message to America,” Sotloff appears in a similar jumpsuit before he is apparently beheaded by a fighter with the Islamic State, the extremist group that has conquered wide swaths of territory across Syria and Iraq and declared itself a caliphate.

In the video, the organization threatens to kill another hostage, this one identified as a British citizen.

In Washington, State Department spokeswoman Jen Psaki said U.S. intelligence analysts will work as quickly as possible to determine if the video is authentic.