The group, called the Ansar al-Sunna Army, posted a written statement on an Islamic Web site claiming that it had killed Lebanese-born
The U.S. military in Baghdad said it was checking into the report of the 24-year-old Hassoun's death but had no confirmation. It was not immediately possible to verify the authenticity of the group's statement.
"We would like to inform you that the Marine of Lebanese origin, Hassoun, has been slaughtered. You are going to see the video with your very eyes soon," said the statement, signed in the name of the group's leader, Abu Abdullah al-Hassan bin Mahmoud.
It also said it had taken another hostage but did not give details.
This, as word came that Prime Minister Iyad Allawi's new government is considering offering amnesty to Iraqi insurgents who fought the U.S.-led occupation, perhaps even pardoning those who killed Americans.
West of the capital, a U.S. Marine died of wounds suffered the day before during operations in Anbar province, the military said. The Marine was the fourth to die this month in Anbar, a Sunni-dominated area that includes Fallujah, Ramadi and Qaim that has been a hotbed of anti-U.S. resistance.
In other developments:
The group claiming it beheaded Hassoun called itself the Ansar al-Sunna Army in Qaim, a town on the Syrian border that has seen frequent clashes between U.S. troops and militants. The message was dated June 20, the day the military said Hassoun, of West Jordan, Utah, was first reported missing - though the posting was dated Saturday.
"We will show a new video of the detention of a new infidel hostage and as recently promised, the beheading of rotten heads," the statement said.
"Withdraw your army and you will be safe. Or else we will keep doing what we are doing."
On June 27, the Arab television station Al-Jazeera broadcast a videotape showing Hassoun blindfolded, along with a statement from militants threatening to kill him unless the United States released all Iraqis in "occupation jails."
In that initial statement, the kidnappers identified themselves as "Islamic Response," the security wing of the "National Islamic Resistance - 1920 Revolution Brigades," referring to the uprising against the British after World War I.
Saturday's claim on Hassoun's death was issued on the same Islamic extremist Web forum where footage was posted last month showing the beheading of U.S. engineer, in Saudi Arabia. The site also often carries claims of attacks by Abu Musab al-Zarqawi, a Jordanian militant said to be operating in Iraq.
Al-Zarqawi's movement claimed responsibility for the, a South Korean who worked for a company delivering supplies to American forces, and , an American businessman, whose body was found in Baghdad in May. Johnson's slaying was claimed by al Qaeda-linked militants in Saudi Arabia, and pictures of his severed head were posted on the Internet.
Another militant group in Iraq claimed last week that it had killed, of Batavia, Ohio, an American soldier held captive since April. The military has not yet confirmed that it was Maupin who was shown in grainy video footage of a man being shot in the back of the head.
In Saturday's statement, the militants said they used a woman to trap Hassoun.
"As your soldier had a love affair with a young Arab woman, he has been lured from the base," the statement said.
The U.S. military said Hassoun had been absent without authorization since June 20, though after the video was shown it changed his status to "captured."
The New York Times, citing a Marine officer speaking on condition of anonymity, has reported that Hassoun had been traumatized by seeing one of his sergeants killed by a mortar, and was trying to make his way back to Lebanon. The officer told the paper that Hassoun sought the help of Iraqis on the base, was betrayed by them and handed over the extremists.
Hassoun's eldest brother, Mohammad, who lives in a Salt Lake City suburb, denied the report. The Marine's relatives were in seclusion at their Utah home after the Web site posting Saturday.
Ansar al-Sunna Army claimed responsibility for the twin suicide attacks on the Patriotic Union of Kurdistan and the Kurdistan Democratic Party offices in Irbil on Feb. 1 that killed 109 people.
As for the possibility of amnesty for insurgents, a spokesman for Prime Minister Allawi, Georges Sada, said Saturday that fighting with U.S. troops was "justified" as resistance to occupation.
"If he (a guerrilla) was in opposition against the Americans, that will be justified because it was an occupation force," Sada said. "We will give them freedom."
Sada added that details of an amnesty were still being worked out and a full pardon for insurgents who killed Americans is a possibility, though not a certainty.
The main thrust of granting amnesty would be to "start everything from new" by giving a second chance to rebel fighters who hand in their weapons and swear off the insurgency, Sada said.
Choking the brutal 14-month insurgency is the No. 1 priority of Allawi's government, and the prime minister is expected to make a number of security-related policy announcements in coming days.
Besides the amnesty plan, those include a new emergency law that sets curfews in Iraq's trouble spots and resurrects of Iraq's death penalty, Sada said.
The U.S. military gave no details of its operations in Anbar province or how the latest Marine to die there was killed. But in Ramadi, an angry crowd of Iraqis held a funeral procession in the streets Saturday, carrying four wooden coffins containing what they said were four Iraqi youths killed in the morning by U.S. tank fire.
The U.S. military called the report "unsubstantiated."