* Journalist Sotloff's family decries 'horrific tragedy'
* U.S. officials do not yet confirm video's authenticity
* Video also threatens man group calls a British hostage
* Group warns other nations off alliance with America (Adds comments from U.S. officials, Sotloff family spokeswoman, further reaction)
By William Maclean
DUBAI, Sept 2 (Reuters) - The Islamic State militant group released a video on Tuesday purporting to show the beheading of a second American hostage, journalist Steven Sotloff, raising the stakes in its confrontation with Washington over U.S. air strikes on its insurgents in Iraq.
A masked figure in the video seen by Reuters also issued a threat against a British hostage, a man the group named as David Haines, and warned governments to back off "this evil alliance of America against the Islamic State".
A statement released by Sotloff's family through a spokesman indicated the family considered the video to be authentic. "The family knows of this horrific tragedy and is grieving privately. There will be no public comment from the family during this difficult time," family spokesman Barak Barfi said.
The purported executioner appeared to be the same British-accented man who appeared in an Aug. 19 video showing the killing of American journalist James Foley, and it showed a similar desert setting. In both videos, the captives wore orange jumpsuits.
In Washington, the White House said it could not immediately confirm the authenticity of the video of Sotloff's beheading. But several U.S. government sources said it appeared to be authentic.
Sotloff, a 31-year-old freelance journalist from Florida, was kidnapped in Syria in August 2013.
"I'm back, Obama, and I'm back because of your arrogant foreign policy towards the Islamic State, because of your insistence on continuing your bombings and in Amerli, Zumar and the Mosul Dam, despite our serious warnings," the masked man said in the video, addressing U.S. President Barack Obama.
"So just as your missiles continue to strike our people, our knife will continue to strike the necks of your people."
In the video, Sotloff describes himself as "paying the price" with his life for the U.S. intervention in Iraq.
Sotloff's mother, Shirley, appealed last Wednesday in a videotaped message to Islamic State's self-proclaimed caliph, Abu Bakr al-Baghdadi, appealing for her son's release.
In the video it released last month, Islamic State said Foley's death was in retaliation for U.S. air strikes on its insurgents who have overrun wide areas of northern Iraq.
The United States resumed air strikes in Iraq in August for the first time since the withdrawal of the final U.S. troops from the country in 2011.
The raids followed major gains by Islamic State, which has declared an Islamic Caliphate in areas it controls in Syria and Iraq.
"We have seen a video that purports to be the murder of U.S. citizen Steven Sotloff by the Islamic State of Iraq and the Levant. The intelligence community is working as quickly as possible to determine its authenticity," White House National Security Council spokeswoman Bernadette Meehan said in a statement.
"If genuine, we are appalled by the brutal murder of an innocent American journalist and we express our deepest condolences to his family and friends. We will provide more information when it is available."
Iraq's outgoing foreign minister, Hoshiyar Zebari, condemned what he called "this savage killing ... an example of savagery and evil," and said it was evidence of the need for Iraq and the West to defeat the Islamic State.
"We have a common enemy and the whole world is moving in the right direction to stop this savagery and brutality," Zebari said. "The whole world is standing united against IS. They must be defeated so these horrid scenes will not be repeated."
Iraqi Shi'ite Muslim politician Sami Askari, who is close to outgoing Prime Minister Nuri al-Maliki, said: "They are trying to scare the Americans not to intervene. I don't think Washington will be scared and stop. ... This is evil. Every human being has to fight this phenomenon. Like cancer, there is no cure. You have to fight it."
British Prime Minister David Cameron condemned Sotloff's apparent decapitation as "an absolutely disgusting and despicable act (by) barbaric terrorists". He said he would hold a meeting of his security crisis team on Wednesday.
French Foreign Minister Laurent Fabius said the killing was a "further illustration of the barbarity without limit of this caliphate of terror that must be fought with the utmost determination".
The video triggered new calls from Obama's critics in the U.S. Congress for him to take more decisive action against Islamic State forces.
"Whenever American air power has been employed, in coordination with reliable partners on the ground, ISIL has been devastated. It's a tactic that should be aggressively pursued both in Syria and Iraq," said Senator Lindsey Graham, a leading Republican voice on foreign policy, using an acronym for the Sunni militant group.
Sotloff's colleagues described him as a dedicated journalist and gifted writer who had filed in-depth reports from across the Middle East. He covered unrest in Libya for Time magazine in 2012 before his kidnapping in Syria.
Time Editor Nancy Gibbs said that Sotloff "gave his life so readers would have access to information from some of the most dangerous places in the world."
On Aug. 24, al Qaeda-linked Nusra Front militants in Syria freed an American writer, Peter Theo Curtis, who had been missing since 2012, following what officials said were efforts by the Gulf Arab state of Qatar to secure his release.
A U.S. government source told Reuters that a criminal investigation being conducted by the Justice Department into the killing of Foley was certain to be extended to include Sotloff.
A person with ties to Islamic State in Diyala province said the group had suffered badly in northern Iraq since U.S. air strikes began last month, ahead of the filmed execution of Foley and grisly video of the beheading of a Kurdish soldier.
"The defeat of the Islamic State in the battle of Mosul Dam contributed to a deflating of the morale of its fighters and the American strikes have also succeeded in restricting their field operations," the man, who spoke on condition of anonymity, said.
"The initiative is not with Islamic State anymore, it's with their enemy now." (Additional reporting by Noah Browning, Mark Hosenball, Ned Parker, Andrew Osborn, Victoria Cavaliere and John Irish; Writing by William Maclean and Will Dunham; Editing by Mark Heinrich and Peter Cooney)