ISIS video shows beheading of American journalist Steven Sotloff

"The family knows of the video and is grieving privately," family spokesman Barak Barfi said.

The killing of Sotloff follows a threat last month by ISIS made during the videotaped beheading of American journalist James Foley. The latest video threatens the life of another man.

A masked ISIS figure in the new video speaks to U.S. President Barack Obama, telling him, "Just as your missiles continue to strike our people, our knife will continue to strike the necks of your people."

The Islamic State has thrived and mutated during the civil war in Syria. It swept into Iraq in June, seizing large swaths of the country's Sunni-dominated northern and western provinces.

Obama ordered targeted airstrikes in Iraq to begin in early August after ISIS fighters began targeting ethnic Yazidis and launching attacks toward the Kurdish regional capital of Irbil.

ISIS appeared to date the execution video of Sotloff, referencing specific U.S. military actions in recent days, including U.S. airstrikes that helped over the weekend to break the siege of Amerli -- a northern Iraqi town home to thousands of minority Shiite Turkmen.

Intelligence officials are analyzing the video, trying to answer some key questions, a senior U.S. administration official said.

Among the questions, the official said: When was it shot? Where was it shot? Is the killer in the Sotloff video the same one in the Foley video?

Until they answer those questions, the official said the administration does not want to speculate.

It's believed ISIS is still holding a "small number" of Americans hostage, said the official, who spoke on condition of anonymity.

In the new video, the militant threatens the life of the man, who is shown kneeling with the militant standing behind him.

"We take this opportunity to warn those governments who've entered this evil alliance of America against the Islamic State to back off and leave our people alone," the militant says.

CNN could not immediately confirm when he was taken captive.

But the Washington Post reported he was an aid worker abducted in March 2013. The newspaper, citing unnamed aid workers involved in efforts to gain his release, said he was abducted near a refugee camp in the northern Syrian province of Idlib.

British Prime Minister David Cameron told reporters he was aware of reports about the video and called Sotloff's killing "an absolutely disgusting and despicable act."

Sotloff disappeared while reporting from Syria in August 2013, but his family kept the news secret, fearing harm to him if they went public. Out of public view, the family and government agencies had been trying to gain his release for the past year.

Last week, Sotloff's mother, Shirley Sotloff, released a video pleading with ISIS leader Abu Bakr al-Baghdadi not to kill her son.

"Steven is a journalist who traveled to the Middle East to cover the suffering of Muslims at the hands of tyrants. Steven is a loyal and generous son, brother and grandson," she said. "He is an honorable man and has always tried to help the weak."

Her plea was met with taunting responses on social media by ISIS supporters.

Sotloff, 31, grew up in South Florida with his mother, father and younger sister. He majored in journalism at the University of Central Florida. His personal Facebook page lists musicians including the Dave Matthews Band, Phish, Miles Davis and movies including "Lawrence of Arabia" and "The Big Lebowski" as favorites. On his Twitter page, he playfully identifies himself as a "stand-up philosopher from Miami."

He graduated from another college, began taking Arabic classes and subsequently picked up freelance writing work for a number of publications, including Time, Foreign Policy, World Affairs and The Christian Science Monitor. His travels took him to Yemen, Saudi Arabia, Qatar and Turkey -- among other countries -- and eventually Syria.

Editor Nancy Gibbs said the magazine's staff is "shocked and deeply saddened" by the reports of his death.

"He gave his life so readers would have access to information from some of the most dangerous places in the world," she said. "Our thoughts and prayers are with him and his family."

Sotloff brings the number of journalists killed in Syria to at least 70, according to the Committee to Protect Journalists.

More than 80 have been kidnapped in Syria since the civil war began, with many going unpublicized, the group said.

"We condemn in the strongest terms possible the murder of journalist Steven Sotloff. He, like James Foley, went to Syria to tell a story. They were civilians, not representatives of any government. Their murders are war crimes and those who committed them must be brought to justice swiftly," CPJ said.

White House spokesman Josh Earnest said the administration "has obviously been watching very carefully since this threat against Mr. Sotloff's life was originally made a few weeks ago."

A top U.S. State Department official told CNN's Christiane Amanpour to "stay tuned" on U.S. plans to combat the organization.

"We are putting the features in place, developing a broad regional coalition, a broad international coalition, working to get a new Iraqi government stood up, working to get our plans in place. So stay tuned," said Brett McGurk, the deputy U.S. assistant secretary of state for Iraq and Iraq.

Obama, who was briefed on the videotaped execution of Sotloff, came under fire from Republicans and Democrats who called on the President to take stronger against ISIS, also known as ISIL.

The criticism came a week after Obama said, "We don't have a strategy yet" to deal with ISIS in Syria. Obama said he has asked America's top defense officials to prepare "a range of options."

"Mr. President, if you can't come up with a strategy, at least tell us what the goal is regarding ISIL," said Sen. Lindsey Graham, R-South Carolina.

Sen. Jeanne Shaheen, D-New Hampshire, said ISIS must be stopped.

"We must use every tool at our disposal, short of introducing ground forces in combat roles, to put an end to the threat they pose to our national security," she said.