The killing was purportedly carried out personally by top terror suspect Abu Musab al-Zarqawi.
In Washington, a U.S. official, speaking on condition of anonymity, said Armstrong's body had been recovered, but the official would provide no information about where or when it had been found.
The taped beheading appears to be of Armstrong, but the CIA is still reviewing the tape to be sure, the official said.
The Tawhid and Jihad group, led by al-Zarqawi, had threatened to behead Armstrong, fellow American Jack Hensley and Briton Kenneth Bigley unless Iraqi women were released by Monday from two U.S.-controlled prisons, including the notorious Abu Ghraib facility.
A militant whose voice resembled al-Zarqawi read a statement in the video saying the next hostage would be killed in 24 hours unless all Muslim women prisoners were released.
In other major developments:
The 9-minute videotape was posted on a Web site used by Islamic militants. It showed a man seated on the floor, blindfolded and wearing an orange jumpsuit with his hands bound behind his back.
Five militants dressed in black stood behind the man, four of them armed with assault rifles, with a black Tawhid and Jihad banner on the wall behind them. The militant in the center read out a statement, as the hostage rocked back and forth and side to side where he sat.
After finishing the statement, the militant pulled a knife, rushed to the hostage from behind and cut his throat until the head was severed.
The victim gasped loudly as blood poured from his neck. His killer held up the head at one point, and placed the head on top of the body.
"The fate of the first infidel was cutting off the head before your eyes and ears. You have a 24-hour opportunity. Abide by our demand in full and release all the Muslim women, otherwise the head of the other will follow this one," the speaker said.
He appeared to indicate the hostages would be killed one at a time and did not specify whether Hensley or Bigley would be next.
The militant on the video called President Bush "a dog" and addressed him, saying, "Now, you have people who love death just like you love life. Killing for the sake of God is their best wish, getting to your soldiers and allies are their happiest moments, and cutting the heads of the criminal infidels is implementing the orders of our lord."
Tawhid and Jihad – Arabic for "Monotheism and Holy War" – has claimed responsibility for at least six hostages, including Armstrong and another American, Nicholas Berg, who was abducted in April. The group has also said it is behind a number of bombings and gun attacks.
Armstrong grew up in Hillsdale, Mich., but left the area around 1990. His work in construction took him around the world; he lived in Thailand with his wife before going to Iraq.
The other American hostage, Jack Hensley, 48, made his home in Marietta, Ga., with his wife Patty and their 13-year-old daughter. Kidnapped with the Americans was Briton Kenneth Bigley, 62. All three worked for Gulf Services Co. of the United Arab Emirates.
Armstrong's slaying came on the heels of the beheading, apparently by another group of Sunni insurgents, of three Kurdish militiamen taken hostage in the north.
More than 135 foreigners have been kidnapped in Iraq, some for lucrative ransoms, and at least 26 of them have been executed. At least five other Westerners are currently being held hostage here, including an Iraqi-American man, two female Italian aid workers and two French reporters.
Despite the unrelenting violence, Prime Minister Ayad Allawi said Sunday that his interim government is determined "to stick to the timetable" of national elections, which are due by Jan. 31.
Last week, U.N. Secretary-General Kofi Annan warned there could not be "credible elections if the security conditions continue as they are now."