French national Hervé Gourdel has been beheaded by the terrorist group Jund al-Khilafah in Algeria, SITE Intel Group and French media report.
The Algerian militant group Jund al-Khilafah took credit for the beheading, and video of the execution has been posted online by SITE.
Gourdel appeared in a video earlier this week in which his captors declared that he had been kidnapped by the ISIS.
The Algerian militants said they were giving French President Francois Hollande 24 hours to stop airstrikes on ISIS or Gourdel would be executed.
French officials have not released any comment on Gourdel's death.
The 55-year-old mountain guide is the fourth Western hostage recently executed by ISIS-linked fighters. The terrorist group has also claimed credit for the killings of two American journalists, James Foley and Steven Sotloff, and British citizen David Cawthorne Haines. ISIS also released a video this week that appears to show it is currently holding British journalist John Cantlie.