The video shows several hostages in orange jumpsuits being led along a beach. A masked militant wearing black is shown walking beside each man. The men are then forced to their knees and their heads are cut off.
One of the militant leaders mentions revenge for the killing of Al-Qaeda leader Osama bin Laden. The makers of the video call themselves the Tripoli Province of the Islamic State group. They are thought to control about one-third of Syria and Iraq.
Terrorists in Libya have been holding 21 Egyptian Coptic Christians for weeks. They had threatened to kill them. A spokesman for the Coptic Church has confirmed the deaths.
The Egyptian government has declared a seven-day period of mourning for the killings. President Abdel Fattah el-Sissi ordered an emergency national security meeting to discuss a response to the killings.
The Islamic State group, also known as ISIL and ISIS, recently released a video that showed the burning of a Jordanian pilot. The group had also released videos to show the beheading of American journalists James Foley and Steven Sotloff, and a French citizen.