The Muntada al-Islam website carried a message from a group calling itself Jaish Ansar al-Sunna - which promised to provide video evidence of Corporal Wassef Ali Hassoun's decapitation.
"We would like to inform you that the marine of Lebanese descent has been killed, and you will soon see the movie with your own eyes," said the statement, signed by Abu Abd Allah al-Hasan bin Mahmud.
The message also alleged that Hassoun was originally captured after he had a romantic liaison with an Arab girl.
The group further claimed it was holding another captive and would soon prove it with the release of a videotape.
The US military in Baghdad said they are aware of the report of Hassoun's death and are checking details but had no comment.
On 27 June, Aljazeera broadcast a videotape showing Hassoun blindfolded, his captors threatening to kill him unless the US released all Iraqis in "occupation jails".
Hassoun was last seen about a week before the videotape was broadcast, the military said.
US forces initially believed the marine may have gone missing, but last month's Aljazeera video had led to the military changing his status to "captured."
AWOL or in a relationship with
The New York Times, citing a marine officer who spoke on the condition of anonymity, has reported on its website that Hassoun had been traumatised after 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 but was tricked by them and handed over to his captors.
But Hassoun's eldest brother, Muhammad, who lives in a Salt Lake City suburb denied the report.