An Algerian Islamist group has released a video showing the beheading of a French tourist.
On September 24, French President Francois Hollande denounced as "cruel and cowardly" the killing of Herve Gourdel, who was kidnapped in Algeria on September 21.
Jund al-Khilafa (Soldiers of the Caliphate), which has pledged allegiance to the Islamic State (IS) group, set a 24-hour deadline for France to halt air strikes on IS targets in Iraq.
France, which launched its first air strikes targeting IS last week, rejected the group's ultimatum.
Addressing the UN General Assembly, Hollande said Gourdel's beheading gives new urgency to stop terrorism and called on other countries to support the fight.
"The fight that the international community needs to wage against terrorism knows no borders," he said.
IS itself has beheaded two American journalists and a British aid worker since August. Their deaths were filmed and posted online.