The Islamic Army of Iraq claims Ronald Allen Schulz, an American adviser, has been killed.
The video does not show the face of the victim, who is seen kneeling with his back to the camera, hands tied behind his back and blindfolded with an Arab headdress.
The videotaped killing showed the man being shot as he kneeled in an open, empty area of dirt. The video also showed Schulz's identity card.
In a separate piece of film, shown on a split screen as the killing was aired, the extremist group also showed a picture of Schulz alive. The group had aired the same footage of Schulz alive when he was first taken hostage earlier this month.
The group first claimed to have killed Schulz in an Internet posting last week. It had said then that it would show the killing.
Schulz, a civilian contractor, has been identified by the extremist group as a security consultant for the Iraqi Housing Ministry, although neighbors and family from Alaska, where he lives, say he is an industrial electrician who has worked on contracts around the world.
Schulz, a native of North Dakota, served in the Marine Corps from 1984 to 1991. He moved to Alaska six years ago, and friends and family say he is divorced.
In other recent developments:
Cheney's visit, under heavy security, was so secret that even Iraq's prime minister said he was surprised when he showed up for what he believed was a meeting with the U.S. ambassador only to see Cheney waiting to greet him.
Cheney toured the country the same day President Bush gaveon Iraq.
"The participation levels all across the country were remarkable," Cheney told reporters after an hour-long briefing from the war's top military commanders. "And that's exactly what needs to happen as you build a political structure in a self-governing Iraq that can unify the various segments of the population and ultimately take over responsibility for their own security."
The vice president visited with Iraq's leaders and military commanders in the Green Zone, saw an Iraqi troop training demonstration at Taji air base, lunched with soldiers who provided security for Thursday's election and gave a speech to troops.
Millions of Iraqis voted Thursday to choose a four-year parliament in an election that passed peacefully around the country. Although no official figures have been released, authorities estimate just under 70 percent of Iraq's 15 million registered voters cast ballots.
The big turnout, particularly among the disaffected Sunni Arab minority that boycotted January's election of a temporary legislature, have boosted hopes that increasing political participation may undermine the insurgency and allow U.S. troops to begin pulling out next year.
Shiites account for about 60 percent of the country's estimated 27 million people, compared with 20 percent for Sunni Arabs. Both Shiite and Sunni political leaders have said they likely will have to form a coalition government together.
Shiite Arabs and Kurds, two groups oppressed under the Sunni Arab-dominated regime of Saddam Hussein, allied to form the interim government that has ruled since last spring.
He saw rows of housing for soldiers at Camp Victory fortified by concrete walls. Smoke for the trash fires burning throughout the occupied city drifted up toward his chopper.
A majority of Americans have said they disapprove of President Bush's handling of the war, and the White House has been pushing back hard against calls for U.S. troop withdrawals.
"You've heard some prominent voices advocating a sudden withdrawal of our forces from Iraq," Cheney told hundreds of American service members gathered to hear a "mystery guest." "Some have suggested that the war is not winnable and a few seem almost eager to conclude the struggle is already over. But they are wrong. The only way to lose this fight is to quit, and that is not an option."
Cheney last visited Iraq in March 1991, when he was defense secretary for Mr. Bush's father, then-President George H.W. Bush. Cheney became the highest-ranking official in the current Bush administration to visit the country since President Bush's unannounced trip on Thanksgiving Day, November 2003.