Lebanon's Foreign Ministry says it believes that a US marine of Lebanese descent has been beheaded by his captors in Iraq.
Hassoun is a Muslim and an Arab, his father points out
The information comes from its diplomatic mission in Baghdad, but there is no final confirmation of Cpl Wassef Ali Hassoun's death.
His death was announced on an Islamic website on Saturday.
The group holding him, Ansar al-Sunna, which is linked to al-Qaeda, said there would be a video showing the beheading.
US officials said they were checking reports that the hostage was dead.
Cpl Hassoun's captors had threatened to kill him unless all Iraqi prisoners held by the US-led coalition forces were released.
The threat was made in a videotape broadcast last Sunday by the Arabic satellite TV channel al-Jazeera, which showed Cpl Hassoun blindfolded.
Relatives of the hostage in West Jordan, Utah, stayed at home with the curtains closed on Saturday.
"I'm speechless. My heart breaks for them," said Karen Sperry, who lives next door to the family.
14 April: Fabrizio Quattrocchi, 36, Italian security guard is shot dead
11 May: Nick Berg, 26, US businessman is beheaded
22 June: Kim Sun-il, 33, South Korean translator is beheaded
29 June: Keith Maupin, 20, US soldier is reportedly killed (not confirmed)
3 July: Cpl Wassef Ali Hassoun, 24, US marine is reportedly beheaded (not confirmed)
A nearby mosque has been holding prayer vigils for Cpl Hassoun who emigrated to the US from the Lebanon four years ago and later obtained US citizenship, according to his father.
His father, who lives in the Lebanese northern port city
of Tripoli called on his captors to release him, as he is a Muslim and an Arab.
The unconfirmed reports of the beheading followed reports that Iraqi Prime Minister Iyad Allawi was considering an amnesty for those who had been fighting the US-led occupation, which could extend to those who have killed Americans.
People who were "in opposition against the Americans, that will
be justified because it was an occupation force," Georges
Sada, Mr Allawi's spokesman, said. "We will give them freedom."
Muslims in the hostage's home town are shocked
Mr Sada added that the purpose was to give rebel fighters a second chance, but that this did not necessarily mean a full pardon.
Cpl Hassoun is believed to have been captured about two weeks ago.
If his death is confirmed, he would be the third hostage, possibly the fourth, to have been killed by militants in Iraq.
Last month, a South Korean translator, Kim Sun-il, was executed by his captors after Seoul rejected their demands for the withdrawal of South Korean troops from Iraq.
American national Nick Berg was beheaded in May by militants who said they were avenging the prisoners abused by US forces in Iraq.
The killing of US soldier Keith Maupin, which was reported last week, has not been confirmed.