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. called 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 against an arid Syrian landscape, 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, David Cawthorne Haines. It was not immediately clear who Haines was.

Britain and France called the killing “barbaric.” British Prime Minister David Cameron said in a statement that he would chair an emergency response meeting with his Cabinet early Wednesday to review the latest developments.

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.

“If the video is genuine, we are sickened by this brutal act, taking the life of another innocent American citizen,” Psaki said. “Our hearts go out to the Sotloff family.”

Psaki said it is believed that “a few” Americans are still being held by the Islamic State. Psaki would not give any specifics, but one is a 26-year-old woman kidnapped while doing humanitarian aid work in Syria, according to a family representative who asked that the hostage not be identified out of fear for her safety.

The fighter who apparently beheads Sotloff in the video calls it retribution for Obama’s continued airstrikes against the group.

“I’m back, Obama, and I’m back because of your arrogant foreign policy toward the Islamic State … despite our serious warnings,” the fighter says. “So just as your missiles continue to strike our people, our knife will continue to strike the necks of your people.”

The killer specifically mentions the recent U.S. airstrikes around the Mosul dam and the beleaguered Iraqi town of Amirli, making it unlikely that Sotloff was killed at the same time as Foley, as some analysts had speculated.

Over the weekend, Iraqi government forces with help from U.S. airstrikes broke the Islamic State’s two-month siege of Amirli, a town where some 15,000 Shiite Turkmens had been stranded.

In a statement Tuesday evening from U.S. Central Command, military officials said an airstrike conducted Monday against Islamic State militants near the Mosul Dam damaged or destroyed 16 armed vehicles.

The SITE Intelligence Group, a U.S. terrorism watchdog, first reported the video’s existence.

In a sign of disorganization — or perhaps dissension — in the extremist group’s ranks, a faction of the Islamic State apparently posted the video early, before it was supposed to be released. In a later Twitter message, those responsible apologized and asked fellow jihadis not to “reproach” them.

The Islamic State has terrorized rivals and civilians alike with widely publicized brutality as it seeks to expand a proto-state it has carved out on both sides of the border. In its rise to prominence over the past year, it has frequently published graphic photos and gruesome videos of bombings, beheadings and mass killings.

Last week, Sotloff’s mother, Shirley Sotloff, pleaded with his captors for mercy, saying in a video that her son was “an innocent journalist” and “an honorable man” who “has always tried to help the weak.”

Sotloff grew up in the Miami area, graduated from Kimball Union Academy, a prep school in New Hampshire, and then attended the University of Central Florida, which said he majored in journalism from 2002 to 2004 but apparently left without graduating.

Just how Sotloff made his way from Florida to Middle East hotspots is not clear. He published articles from Syria, Egypt and Libya in a variety of publications. Several focus on the plight of ordinary people in war-torn places.

In a statement, Foreign Policy magazine said it was saddened by news of his death and called him a “brave and talented journalist” whose reporting “showed a deep concern for the civilians caught in the middle of a brutal war.”

Time Editor Nancy Gibbs said Sotloff “gave his life so readers would have access to information from some of the most dangerous places in the world.”

House Foreign Affairs Chairman Rep. Ed Royce, a California Republican, said the new video demonstrates the Islamic State’s “barbarity across the region — beheading and crucifying those who don’t share their ideology.” He said the U.S. and allies need to step up military action against the group, including through airstrikes.

At Sotloff’s parents’ home in Pinecrest, Florida., two police vehicles blocked the driveway Tuesday, and officers advised journalists to stay away. Friends of the family could be seen coming and going.

“Everyone’s been concerned. Everyone is grieving,” neighbor Pepe Cazas said. “It’s terrible. I’ve been praying for him.”