An Algerian jihadist group has released a video that appears to show the beheading of French tourist Herve Gourdel, who was seized on Sunday.
Militant group Jund al-Khilafa had set a 24-hour deadline on Tuesday for France to halt air strikes in Iraq.
Mr Gourdel, 55, was abducted in the north-east Kabylie region.
France joined the US last week in launching air strikes on Islamic State (IS) militants in Iraq but did not take part in the strikes on IS in Syria.
French President Francois Hollande and his Prime Minister, Manuel Valls, publicly rejected the group’s ultimatum on Tuesday.
The video of Mr Gourdel apparently being killed was entitled “Message of blood for the French government”, reports said.