CAIRO: Egypt's leader vowed to punish the "murderers" responsible for the beheading of 21 Egyptian Christians after the Islamic State group in Libya released a video on Sunday purportedly showing the mass killing.

A visibly angry President Abdel Fattah al-Sisi said Egypt "reserves the right to respond in a suitable way and time" in a televised speech, and declared seven days of mourning after the video was distributed by jihadists on social media.

The footage shows 21 handcuffed hostages wearing orange jump suits being beheaded by their black-suited captors on a beach the group said was in the Libyan province of Tripoli.

In the latest issue of the IS online magazine Dabiq, the group had said the same number of Egyptian hostages were being held in Libya.

The Egyptian leader also called a meeting of a top security body in Cairo that includes his defence and interior ministers along with top military figures.

The White House led condemnation of the apparent beheadings, describing the killers as "despicable" and adding that the brutality shown "further galvanises the international community to unite against ISIl," an alternative acronym for the group.

IS militants have been hammered by US-led air strikes in Iraq and Syria after taking over swathes of the two countries, and the group has active affiliates in Egypt and Libya.

The Coptic Church issued a statement saying it was "confident" the Christians' killers would be brought to justice as it confirmed those beheaded were Egyptian Copts.

Al-Azhar, the prestigious Cairo-based seat of Islamic learning, denounced the "barbaric" killings.

Egyptian state television broadcast some of the footage from the IS video without showing the beheadings but depicting the hostages being marched along by their captors on a beach.

Sunday's video, entitled "A message signed with blood to the nation of the cross", has a scrolling caption in the first few seconds referring to the hostages as "people of the cross, followers of the hostile Egyptian Church".

The IS branch in Libya had claimed in January to have abducted 21 Christians.

Copts' killings a 'revenge'

Egypt last year denied reports of having carried out air strikes on Islamists in Libya, but US officials said its ally the United Arab Emirates carried out the strikes using Egyptian bases.

French President Francois Hollande, whose government is poised to sign a deal selling Egypt advanced Rafale fighter jets on Monday, expressed his "concern at the expansion of Daesh in Libya," using another name for the Islamic State group.

Libya's embattled parliament, which is locked in a conflict with Islamist militias, expressed its condolences in a statement and called on the world to "show solidarity with Libya" against militants.

The video makes reference to Egyptian women Camilia Shehata and Wafa Constantine, the wives of Coptic priests whose alleged conversion to Islam sparked a sectarian dispute in Egypt in 2010.

After the beheadings, a scrolling caption on the footage said: "The filthy blood is just some of what awaits you, in revenge for Camilia and her sisters."

Shehata went missing for five days in July 2010 after a domestic argument before police found her and escorted her back home.

When she disappeared, Coptic Christians staged protests, but when she was returned, Islamists took to the streets alleging she had chosen to convert to Islam and was being held by the church against her will.

Wafa Constantine also went missing, in 2004, reportedly after her husband refused to give her a divorce. She was temporarily sequestered at a convent as reports of her conversion to Islam were circulated.

The latest IS video comes just days after the jihadists released footage showing the gruesome burning alive of a Jordanian pilot the group captured after his F-16 came down in Syria in December.